My Google Scholar Profile

About Me

Education

M.A.(1976)
University of Indore

M.Phil. (1978)
University of Kurukshetra

Post Graduate Diploma in Computer Science (February 1987)
University of Sydney

Ph.D. (August 1987)
University of Sydney

Awards and Honors

FTICA (1990)
Founding Fellow of the Institute of Combinatorics and its Applications
Distinguished Achievement Award, 1998 (Gordon Jones Award)
School of Science and Mathematics, College of Charleston
College of Charleston Distinguished Research Award, 1998
Outstanding Male faculty member 2000-2001
Zeta Phi Beta Sorority, Chi Iota Chapter
College of Charleston Distinguished Advising Award, 2001
College of Charleston recognition of initiatives promoting undergraduate research, 2002
AMP Outstanding Service Award, 2002
Departmental Special Recognition November 4, 2002 (Service)
Departmental Special Recognition Feb 2003 (Student Research)
Leo I. Higdon Jr. Presidential Legacy Award for outstanding leadership, May 2007

Hugh Kelly Fellow, Rhodes University, South Africa, Summer 2010 (Fellowship for Senior Scientists)

Fulbright Scholar, Uganda, 2014-15

Fulbright Specialist, Uganda, 2016-17

Michael J. Auerbach Award for Excellence in Student Research Mentorship, 2018-19

Fulbright Specialist, Thailand, 2022

Research and Teaching Experience

Emeritus Professor of Mathematics, College of Charleston
May 2022 -
Professor of Mathematics, College of Charleston
May 2007 - May 2022
Hugh Kelly Fellow, Rhodes University, S. Africa
May 15 - August 15, 2010
Professor and SC-AMP Director, College of Charleston
August 1999 - May 2007
Associate Professor, College of Charleston
September 1992 - August 1999
Visiting Professor, University of Bombay
July 1995 - April 1996

Assistant Professor, College of Charleston
September 1988 - August 1992

Lecturer, University of Papua New Guinea
June 1987 - August 1988

Professional Activities

Guest Editor:
1. Discrete Mathematics issue in Honor of Professor Jennifer Seberry
2. JCMCC issue for 2007 Midwest Conference on Combinatorics, Cryptography, and Computing
Member of Council:
Institute of Combinatorics and its Applications
Refereed for various international journals such as ARS Combinatoria, JCMCC, JCT, Bulletin of the ICA, Ultilitas Mathematica, etc.
Examiner or on the Ph.D. committee of many students from the USA and abroad

Ph.D. Students

The following is a partial list of Ph.D. students I supervised.

Kasifa Namyalo, Group divisible designs: existence results for block size 3,4, and 5, Mbarara University of Science and Technology, 2019

Dinkayehu Mengesha Woldemariam, New group divisible designs with block size four and five, Adama Science and Technology university, 2022

Anilchandra Jha, The role of Bhaskaracharya in chronological development of Mathematics, Nepal Sanskrit University, 2023

Parshuram Chaudhary, A study of Ethnomathematical aspects on Special reference to Tharu's community, Nepal Sanskrit University, 2023

Zebene Girma Tefera, New existence results on group divisible designs and 3-GDDs, University of Addis Ababa, 2024

Sample of Courses Taught and/or Designed

Algebra
Applied Algebra
Coding Theory
Combinatorics
Discrete Mathematics 1 and 2

Discrete Modeling

Design Theory with Applications in Error Correcting Codes

Elementary Statistics

Graph Labeling (Independent Study)

Linear Algebra

Real Analysis

Memberships

Life Member, Combinatorial Mathematics Society of Australasia
Life Member, Indian Academy of Mathematics, India
Life Member, Forum for Interdisciplinary Mathematics
Life Member, Institute of Combinatorics and its Applications (since 1990)
Life Member, Mathematics Consortium

Refereed Research Publications

1. A note on strongly regular Hamiltonian equivalence of K2n and K2n-1,2n-1 and its generalization, J. Indian Acad. Math., 5, 1983, 65-67, India.
2. All directed GDDs with block size three, l1=0, exist, Utilitas Mathematica, 26, 1984, 311-317, Canada.
3. Non-existence of certain GBRDs, Ars Combinatoria, 18, 1984, 5-20, with W. de Launey, Australia-Canada.
4. Generalized Bhaskar Rao designs of block size 3 over Z4, Ars Combinatoria, 19A, 1985, 273-286, with W. de Launey and J. Seberry, Australia-Canada.
5. Some results on directed and cyclic designs, Ars Combinatoria, 19A, 1985, 179- 190, Australia-Canada.
6. A note on equi-neighboured block designs, Utilitas Mathematica, 28, 1985, 91- 98, Canada.
7. Block designs without repeated blocks, Ars Combinatoria, 21, 1986, 71-87, Australia-Canada.
8. All simple BIBDs with block size 3 exist, Ars Combinatoria, 21A, 1986, 257-270, Australia-Canada.
9. On a BIBD construction, Ars Combinatoria, 22, 1986, 165-169, AustraliaCanada.
10. Encryption methods based on combinatorial designs, Ars Combinatoria, 21A, 1986, 237-246, with Jennifer Seberry, Australia-Canada.
11. On weighing matrices with square weight, Proceedings of the symposium on optimization, Design of experiments and Graph Theory, I.I.T. Bombay, Dec. 15- 17, 1986, 71-76, with Jennifer Seberry, India.
12. Colourable designs, new group divisible designs and pairwise balanced designs, J. Stat. Planning and Inference, 15, 1987, 379-389, with C.A. Rodger and Jennifer Seberry, USA.
13. Encryption method using Hungarian rings, Applied Discrete Mathematics, 16, 1987, 151-155, with Joseph Hammer, U.S.A.
14. A note on orthogonal designs, Ars Combinatoria, 24, 1987, 93-100, with J. Hammer and Jennifer Seberry, Australia-Canada.
15. On the union-closed sets conjecture, Ars Combinatoria, 27, 1989, 149-154, with J-C. Renaud, Australia-Canada.
16. A new construction of balanced ternary designs, Utilitas Mathematica, 36, 1989, 45-47, Canada.
17. Constructions of balanced ternary designs, Journal of the Australian Mathematical Society, 48, 1990, 320-232, Australia.
18. On PBIBD constructions using t-designs, Ars Combinatoria, 29, 1990, 21-23, Australia-Canada.
19. Improved bounds for the union-closed sets conjecture, Ars Combinatoria, 29, 1990, 181-185, with J-C. Renaud, Australia-Canada.
20. Highly quantized realizations of the digital filter system matrix, The Journal of the Franklin Institute, 327, No. 6, 867-875,1990, with T. Bose.
21. Periodic and nonperiodic modes in two dimensional digital filters, The proceeding of the ISCAS. 90, 2998-3001,1990, with T. Bose.
22. Bhaskar Rao ternary designs and applications, The Australasian Journal of Combinatorics, 3, 165-190, 1991.
23. Two constructions for µ-resolvable ternary designs, with Margaret Francel, Congressus Numerantium, 85, 1991, 51-63.
24. A construction of balanced ternary designs based on SBIBDs, with Margaret Francel, Utilitas Mathematica, 39, 1991, 87-189.
25. Row-column directed designs, with Rose Hamm, Discrete Mathematics, 92, 321- 328, 1991. Reprinted in Selected Papers in Combinatorics, Topics in Discrete Mathematics, 2, 321-328, 1992.
26. Classification and constructions of ternary group divisible designs, with William A. Denig, Congressus Numerantium, 90, 1992, 129-140
27. Remarks on R.G. Stanton's results, with Joseph Hammer, Discrete Mathematics, 102, 149-154, 1992.
28. Some necessary existence conditions, constructions and a list of partially balanced ternary designs, with Jaideep Mirchandani, Congressus Numerantium, 96, 165- 183, 1993.
29. A note on Union-closed sets conjecture, with R. M. Norton, the Journal of Australian Mathematical Society, 55, 411-413, 1993.
30. Constructions of balanced ternary designs based on Generalized Bhaskar Rao designs, with Jennifer Seberry, Journal of Statistical Planning and Inference, 34, 423-432, 1993.
31. On row-column directed block designs, with Rose Hamm, the Australasian Journal of Combinatorics, 8, 1993, 123-126.
32. A Comparison of n-ary design definitions, with Margaret Ann Francel, Ars Combinatoria, 38, 1994, 77-86.
33. A note on small defining sets for some SBIBD(4t-1,2t-1,t-1), with Jennifer Seberry, Bulletin of the ICA, 10, 1994, 26-32.
34. Ternary designs with more than one replication number, with Margaret Francel, Congressus Numerantium, 101, 1994, 17-25.
35. Note on parameters of balanced ternary designs, Australasian Journal of Combinatorics, 11, 1995, 177-179.
36. An application of symmetric chains to a statistical database compromise prevention problem, with Kevin Miller, Bulletin of the ICA, 13, 1995, 57-64.
37. On ternary designs with a specific number of blocks with repeated elements, with Thomas Kunkle, Ars Combinatoria, 40, 1995, 129-142.
38. Certain parametric relationships and nonexistence results for affine m-resolvable balanced ternary designs, with M. Francel, the Journal of Combinatorial Math. and Combinatorial Computing, 17, 1995, 89-96.
39. Constructions for Dr = 2 and general Tocher ternary designs, with Margaret Francel, Congressus Numerantium., 110, 1995, 121-128.
40. Balanced part ternary designs: a parameter list, with Thomas Kunkle, "the CRC Hand book on Design Theory", 1996, 233-238.
41. Balanced part-ternary designs: new results and constructions, with Thomas Kunkle, the Journal of Combinatorial Mathematics and Combinatorial Computing, 22, 1996, 3-12.
42. Ternary 1-designs(V,B,r1,r2,R;K), with W. Hugh Haynsworth, Utilitas Mathematica., 50, 1996, 103-112.
43. Simple and irreducible group divisible designs with block size 3, with Vasanti N. Bhat-Nayak, Congressus Numerantium., 114, 1996, 179-192.
44. Ternary designs with the maximum or near maximum number of replication numbers, with Margaret Francel, Australasian Journal of Combinatorics., 13, 1996, 283-294.
45. On r-extendability of the hypercube Qn, with Nirmala B. Limaye, Mathematica Bohemica., 122, no. 3, 1997, 249-255.
46. (D;4)-cages : some new results with Nirmala B. Limaye and Margaret Francel, Congressus Numerantium, 126, 1997, 73-85.
47. A family of connected quasi-strongly regular graphs, with W. L. Golightly and W. H. Haynsworth, Congressus Numerantium, 124, 1997, 89-95.
48. GDDs, GBRDs and Generalized weighing matrices, with Jennifer Seberry, Utilitas Mathematica, 54, 1998, 157-174.
49. One and two-block configurations in balanced ternary designs, with Margaret Francel, Ars Combinatoria., XLVIX, August 1998, 217-224.
50. Some constructions of block designs, with Malcolm Greig, Journal of combnatorial Mathematics and Combinatorial Computing, 28, 1998, 149-160.
51. A symmetric difference construction of strongly regular graphs, with W.L. Golightly and W.H. Haynsworth, Bulletin of the ICA, 24, 1998, 51-56.
52. (D;n)-cages with |D| = 2,3,4, with Nirmala Limaye, Congressus Numerantium 133, 1998, 7-20.
53. Nontransitive semi-standard orthogonal Latin squares, with W.L. Golightly and W.H. Haynsworth, Bulletin of the ICA, 25, 1999, 88-94.
54. On F-squares and their critical sets, with L Fitina and Jennifer Seberry, Australas. J. Comb. 19, 1999, 209-229.
55. The existence of group divisible designs with first and second associates, having block size 3, with Hung-Lin Fu and C.A. Rodger, Ars Combinatoria, 54, 2000, 33- 50.
56. On c-Bhaskar Rao Designs, with Spencer Hurd, Journal of Statistical Planning and Inference, 90, 2000, 161-175.
57. All c-Bhaskar Rao designs with block size 3 and c greater or equal to -1 exist, Ars Combinatoria, 59, 2001, pp. 21-32.
58. On c-Bhaskar Rao designs with block Size Three and Negative c, With Spencer Hurd, Journal of Combinatorial Mathematics and Combinatorial Computing, 38, 2001, 21-32.
59. A 2 by 2 by 2 grid design, with Yukiyasu Mutoh, Congressus Numerantium, 149, 2001, 193-199.
60. On enclosing BIBD(v,3,l) into BIBD(v+1,3,l+1), with Spencer Hurd, Bulletin of the ICA, 36, 2002, 46-52.
61. On c-Hadamard Matrices, with Spencer Hurd, Ars Combinatoria, 63, 49-64, 2002.
62. On c-Bhaskar Rao Designs with Block Size 4, with Spencer Hurd and Malcolm Greig, J. Combinatorial Designs, 10, 2002, 361-386.
63. Minimal enclosings of triple systems I: adding one point, with S. Hurd and P. Munson, Ars Combinatoria, 68, 2003, 145-159.
64. Minimal enclosings of triple systems II: with S. Hurd. ARS Combinatoria, 68, 2003, 263-282.
65. Embeddings and faithful enclosings of GDD’s with a constant number of groups, with Spencer Hurd, The Australasian Journal of Combinatorics, 27, 2003, 213- 222.
66. Linear Codes through Latin Squares modulo n, with Alexander L Strehl, Bulletin of the ICA, 37, 2003, 73-81.
67. An application of partition of indices to enclosings of triple systems, with Spencer Hurd, Discrete Mathematics, 261, 2003, 337-346.
68. Faithful enclosings of group divisible designs formed by adding an additional group, with S. Hurd and Tarsem Purewal, Congressus Numerantium, 161, 2003, 129-138.
69. Minimal enclosings of group divisible designs with block size 3 and group size 2, with Hurd and Purewal, J. Combin. Math. Combin. Comput. 46, 2003, 205-225.
70. General constructions of c-Bhaskar Rao designs and the (c, L) spectrum of a cBRD, with Hurd, S.P., and M. Greig, Discrete Mathematics, 274,1-3, 2004, 77- 92.
71. Regular and strongly regular Planer graphs, with N. Limaye, P. Stanica, P. Young, J. Combin. Math. Combin. Comput., 54, 2005, 111-127.
72. On c-Bhaskar Rao designs and tight embeddings for path designs, with S.P. Hurd, Discrete Math, 308, 2008, 2659-2662.
73. Odd and even Group Divisible Designs with Two groups and Block Size Four, with S.P. Hurd, Discrete Math., 1-3, 284, 2004, 189-196.
74. The anatomy of a design with M.A. Francel, S.P. Hurd, G.L. Rudolph, Congressus Numerantium 181, 2006, 77-88.
75. Pair resolvability and Tight embeddings for Path Designs, with Spencer Hurd, JCMCC 58, 2006, 113-127.
76. A family of group divisible designs of block size four and three groups with l1 = 2 and l2=1 using MOLS, with Devin Henson, Ars Combinatoria, 78, 2006, 123- 125.
77. A new construction for Group Divisible Designs with Block size Five and Few Groups, with S. P. Hurd, and Nutan Mishra, ARS Combinatoria, 84, 2007, 243- 245
78. An edge-coloring problem For Designs, with Spencer Hurd, Bulletin of the ICA, 49, 2007, 15-20.
79. A new Type of Block Design, with William Beam, Bulletin of the ICA, 50, 2007, 26-28.
80. The non-existence of (n-2)-SB(n,n-1) adesigns and some existence results, with William Beam, the Bulletin of the ICA, 51, 2007, 73-79.
81. A Construction For Group Divisible Designs with Two groups, with Narong Punnim, Congressus Numerantium, 185, 2007, 57-60.
82. Group divisible designs with three groups and block size four, with Devin Henson and Hurd, Discrete Math., 307, 2007, 1693-1706.
83. Balanced Ternary Designs, with Spencer Hurd, "the CRC Hand book on Design Theory", 2007, 330-332.
84. On Balanced Index Sets of One-Point Unions of Graphs, with Harris Kwong, SinMin Lee, JCMCC, 66, 2008, 113-127.
85. A note on Non-Regular Planar Graphs, with Nutan Mishra, Adrienne Chisolm and Jesse J. Raab, JCMCC, 66, 2008, 17-31.
86. Group divisible designs with block size four and two groups, with Spencer Hurd, Discrete Math., 308, 2008, 2663-2673.
87. Group Divisible designs with two groups and block configuration (1,4), with Spencer Hurd, Journal of Combinatorics, Information and System Sciences, 32, No 1-4, 2007, 297-306.
88. Group divisible designs with two groups and block size five with fixed block configuration, with S. Hurd and Nutan Mishra, JCMCC, 70, 2009, 15-31.
89. Embedding multiple BIBDs into BIBDs or Projective planes, with Spencer Hurd, Journal of Statistics and Applications, 4, No. 2-3, 2009, 277-284.
90. Beautifully Ordered Balanced Incomplete Block Designs, with Hau Chan, JCMCC, 74, 2010, 65-81
91. Sets of MOLSs generated from a single Latin square, with Hau Chan, Congr. Numer., 195, 2009, 115-123.
92. A non-existence result and large sets for Sarvate-Beam designs, with Hau Chan, Ars Combin. 95, 2010, 193-199.
93. It’s hard to be different, with Peter Dukes and Spencer Hurd, Bulletin of the ICA 60, 2010, 86-90.
94. Loop designs, with Hurd and Punnim, JCMCC, 78, 2011, 261-272.
95. Cyclic Loop Designs, with Hurd, JCMCC, 78, 2011, 111-117.
96. Restricted Simple 1-designs, with Wanida Hemakul and Chaiwoot Moolsombut, JCMCC, accepted
97. On 1-sarvate-beam designs, with Hau Chan, Discrete Mathematics, 311, 2011, no. 10-11, 856-865.
98. Stanton graph decompositions, with Hau Chan, Bulletin of the ICA, 64, 2012, 21- 29.
99. Group divisible designs with two association classes, with Chaiyasena, A.; Hurd, Spencer P.; Punnim, Narong; J. Combin. Math. Combin. Comput. 82 (2012), 179– 198.
100.Sarvate-beam designs: new existence results and large sets. With H. Chan, D. Hein J. Combin. Math. Combin. Comput. 83 (2012), 211–216.
101. Decomposition of a λ Kv into equal number of K3s and P3s, with Li Zhang, Bull. Inst. Combin. Appl. 67 (2013), 43–48.
102.Embedding into complements!, with A Shealy Bull. Inst. Combin. Appl. 67 (2013), 73–80.
103.Decomposition of a 3K8t into H2 graphs, with Li Zhang Ars Combin. 110 (2013), 23–32.
104.Further existence results on beautifully ordered balanced incomplete block designs, with G. Mitchener and A. Shealy J. Combin. Math. Combin. Comput. 86 (2013), 151–161.
105.Decomposition of λKv into multigraphs with four vertices and five edges, with Sarah Malick J. Combin. Math. Combin. Comput. 86 (2013), 221–237.
106. Two Combinatorial Question, with Li Zhang, Bull. Inst. Combin. Appl. 70 (2014), 45-56.
107.New Construction Techniques for H2(8t,3)s, with Li Zhang, J. Combin. Math. Combin. Comput. 90 (2014), 11-19.
108.DecompositionsofλKn usingStanton-typegraphs,withDerekHein,J. Combin. Math. Combin. Comput. 90 (2014), 185-195.
109. DecompositionofλKnintoS(4,3)'s.,withD.Hein,JCMCC,94,(2015)3-14.
110.Decomposition of a 2K_{10t+5} into H_3 graphs, with Zhang, L. JCMCC, 94, (2015), 53-59.
111.Decomposition of a 2K_{10t} into H_3 graphs, with L. Zhang, ARS Combinatoria, (2015), 121, 315-319.
112.GDD(n,2,4;λ 1,λ 2) with equal number of even and odd blocks, with Issa Ndungo, Discrete Mathematics, 339, (2016), 1344-1354.
113.Group Divisible Designs of four groups and block size 5 with configuration (1,1,1,2)., with Ronald Mwesigwa and Li Zhang, Journal of Algebra Combinatorics Discrete Structures and Applications, 3(3), (2016), 187-194.
114.A fundamental theorem of multigraph decomposition of a λKm,n, with Paul Winter and Li Zhang, JCMCC, 96, (2016), 201-216.
115. Graph decompositions of K(v, λ) into modified triangles using Langford and Skolem sequences, with Spencer hurd, Ars combinatoria, 129, (2016), 403-416.
116.On perfect MRDs, with Shahab Faruqi, Bull.Inst. Combi. Appl. 78 (2016), 23- 40.
117. Decomposition of a λKm,n into graphs of four vertices and five edges, with Winter and Zhang, JCMCC, 98 (2016), 139-150.
118. Group divisible designs of three groups and block size five with configuration (1,2,2), with Zhang, Australas. J. Combin. 66 (2016) 333-343.
119.GDD(n1,n2,3; λ1, λ2) with equal number of blocks of two configurations, with B. Billings and K. Namyalo, JCMCC, 102 (2017), 19-44.
120.Decompositions of λKn into LOE and OLE graphs. With Li Zhang, Ars combinatoria, 133 (2017) 93-105.
121.3 -GDDs with block size 4, with Wilbroad Bezire, Bull. Inst. Combi. Appl. 82, (2018), 50-65.
122. Group divisible designs with block size 4 and number of groups 2 or 3, with Mary Nanfuka, Ars Combin., 141, (2018), 229-241
123. On edge decompositions of a complete graph into smaller complete graphs, with Faruqi and Katre, JCMCC, 106 (2018), 83-107.
124. Decomposition of λKv into multigraphs with four vertices and five edges.With Faruqi and Katre, Ars Combin. 136, (2018), 287-316.
125. Group divisible designs with block size five from Clatworthy's table, with Mishra and Namyalo, Comm. Statist. Theory Methods, 41 (2018), no 9, 2085-2097.
126. A simple Construction of 3GDDs with block size 4 using SQS(v), with W Cowden, Bulletin of the ICA, 84 (2018), 40-44.
127. GDD(n1,n,n+1,4;λ1,λ2): n1=1or 2, with Namyalo, Kasifa; and Zhang, Li J. Combin. Math. Combin. Comput. 110 (2019), 19–37.
128. EGDD(n1+n2,3;λ1,λ2) for n1=2 and n1=5. With Blaine Billings and Kasifa Namyelo , Ars Combin. 150(2020) 281–293.
129. Pairwise and variance balanced n-ary block designs, with Mishra, Nutan J. Combin. Math. Combin. Comput. 114 (2020), 307–328.
130. A short note on 3-GDDs with 3 groups and block size 4, with Shinde, Pramod N.J. Combin. Math. Combin. Comput. 114 (2020), 329–339.
132. 3−GDD(n1,n2,4;Λ1,Λ2) with Zhang, LiJ. Combin. Math. Combin. Comput. 114 (2020), 341–352.

133. Missing blocks of two designs in Hanani's paper with Shinde, Pramod N. Bull. Inst. Combin. Appl. 94 (2022), 73–78

134. A note on GDD(1,n,n,4;λ1,λ2), with Woldemariam, Dinkayehu M., J. Algebra Comb. Discrete Struct. Appl. 9 (2022), no. 2, 85–99.

135. 3-group divisible designs with 3 groups and block size 5, with Girma Tefera, Zebene; and Asefa Fufa, Samuel, J. Math.(2023), Art. ID 1010091, 8 pp.

136. On constructions of GMGDs, with Worawiset, Somnuek and Zhang, Li Util. Math. 119 (2024), 51–61.

137. A variation on 3-GDDs 3-GDDs with blocks of size 4 and 3 groups, with Trubey, JCMCC, accepted 8/1/2020

Other Publications

1. An application of graph representation of designs, with Joseph Hammer, Bulletin of the Institute of Combinatorics and its Applications, 3, 107-108, 1991.

2. Another application of graph representation of designs, with Joseph Hammer, Bulletin of the ICA, 6, 1992, 61-62.

3. Suggestions for presentation of a twenty-minute talk, with Jennifer Seberry, Bulletin of the ICA, 4, 1992, 90-91.

4. Substance abuse prevention curriculum module: Know Your Class and Help Your College, published by Network for dissemination of Curriculum Infusion (NDCI).

5. Winter, P A and Sarvate, D G, H-Eigen Energy Formation Number of HDecomposable Classes of Graphs- Formation Ratios, Asymptotes and Power. Advances in Mathematics: Scientific Journal. 3(2) (2014), pp 133-147.

Presentations at Conferences

I have presented at numerous international and national conferences in countries including Australia, China, Greece, India, Japan, New Zealand, Singapore, Uganda, and the USA. I have also chaired sessions at various conferences and delivered one-hour invited talks at multiple universities in India, Japan, Papua New Guinea, China, and the USA.

For example, I gave an hour-long talk at Shanghai Jiao Tong University in China during the summer of 2002, and chaired a session at the Midwestern Conference on Combinatorics, Cryptography, and Computing in 2001, 2003, and 2006. I was an invited speaker at the Nineteenth Clemson MiniConference on Discrete Mathematics and Related Fields in 2004, and at the Discrete Mathematics conference at Sri Nakharinwirot University, Bangkok, Thailand in 2006 and 2007.

I was invited to give a one-hour presentation at a Design Theory Conference in Gainsville, NC, USA in October 2007 but I was unable to attend as I was organizing a conference in Charleston at the same time. Similarly, I was not able to attend an invited talk at a conference in Canada which was organized to honor Professor Hadi Kharaghani, and twice in Myanmar.

In 2016, I gave a talk at Auburn during a conference to honor Professor Chris Rodger and organized the 29th Midwestern Conference on Combinatorics, Cryptography, and Computing in October 2015. I also gave two invited talks at two universities there.

I was a plenary speaker in October 2018 at a high-profile International Conference on Mathematics in Laos.

As for workshops, I have conducted several for mathematics teachers. In the summer of 2006, I taught three weeklong full-day workshops on Discrete Mathematics, Statistics, and Design Theory, followed by a weeklong full-day workshop on Graph Theory and Problem Solving in the summer of 2007 in Thailand. I am particularly pleased with how the Discrete Math and graph theory workshops have empowered teachers with more problem-solving skills and provided real-world applications of mathematics.

In 2009, I held another Design Theory workshop at SriNakharin University and also a 5-hour workshop at Neresuan University, both in Thailand. As a Fulbright scholar in Uganda in 2014-15, I conducted workshops on teaching portfolio and Discrete Mathematics, and in 2017 as a Fulbright specialist, I taught research supervision and involving students in research.

Student Research

Just like my talks at conferences or departmental talks at COFC or other places, I do not keep a list of students I have worked with them on large projects, bachelor’s essays, or research publications or smaller projects where they only do oral presentations or posters for the class or in a conference or send correct solutions of challenging problems in math magazines before the deadline to get their names published. All my mentees get a good practice of how math is created and a good experience including communicating difficult ideas to a live audience and for publications and a bit of life advice.

Projects: As mentioned earlier, I asked many students, including Jim Bowring, Lauren Tubbs, Gary Phelp, and William Bernard to solve these kinds of problems from Math Horizons, the American Mathematical Monthly, or the College Mathematics Journal. These short-term projects have all the components of writing research papers and doing research albeit on a much smaller scale and time commitment. Dorothy Chappell did a project where we did not publish on her main project, did solve a problem. Long Projects are the projects which end up in refereed publications.

Instead of listing names and project titles, I discuss my work with students: I have a solid experience working and mentoring with students of different levels and majors. The best way to mentor students is to get them involved in working with the faculty outside their coursework. That is where one can help them to set goals and mentor. Though calling the process “research” is more popular and accepted in higher education and liked by the students.

First Year Non-Math Major Students: Due to some rules and regulations, e.g., IRB, I stopped mentoring Math 104 (Elementary Statistics) or 103 students, but in 1998 and 2001 eight of them did poster presentations at the SSM poster session with great interest from the visitors on drug and alcohol use. Katherine Coffey, probably an Arts major, did a project and in-class presentation in Math 103 (a course for non-math students) on “Introduction to Perspective and Space Coordination”. Witold Witkowaski did a project on the ratio of height, weight, length, and width of faces of the models to see the connection with Beauty and Golden ratio. He also did a presentation and poster.

High School Students: In 2009, I mentored twenty bright students from a very prestigious and selective school on eight projects in Thailand in one month: I worked with them from 8 AM to 6 PM, one group after another, with only breaks for food. In the end, all of them did presentations for the school with professors from nearby universities in attendance. I mentioned one of the group’s new results in a MathSciNet review. Sarah Malick, M. king, Blaine Billing were from the SC Governor’s school for Science and Mathematics. All of them presented their work in their School’s required presentations, but also at Conferences. Sarah was even invited by USC Columbia graduate students’ seminar. Sarah and Blaine both published with me.

Minority Students: I have worked from August 1999 to May 2007 as the campus director of a minority program (SC-AMP) where I worked with students of many different backgrounds, needs, and culture and was able to instill in them a desire to succeed and to progress. Not counting students from other STEM majors, I mentored many minority students in Mathematics, including Adrienne Chisholm, Design theory; Freda McInnis, Magic squares; Tracy Gunter, GDDs and helped her presentation for another number theory project from Auburn REU; Troy Nelson, Combinatorial problems; Vashtia Bannett On Magic squares, she won a prize in presentation just like Tracey, Troy, and Adrienne in conferences.

Independent Studies and Bachelor’s Essays: Cryptography Jaideep 90-91, Group divisible designs, Laura Boehm and Barbara Pond on Error Correcting Codes, Brittney Johnson (minority) 2015-16, on applications of algorithms in remote sensing Ashleigh 2018, 3- GDDs Aidyn Trubey 2019, and many others. Independent studies may lead to a research project or Bachelor’s essay: In turn, Bachelor’s essays, for example, with Hau Chan, Devin Henson, Alex Strehl, Semmy Purewal, and William Beam, produced multiple published papers. The latest independent study by Aidyn Trubey on “3-GDDs a survey and new results” has produced only one accepted paper but at least three presentations including one on a short-term project “Knight’s tour”.

Master’s and Ph.D. Students: I teach at a mainly teaching and undergraduate College. We call ourselves College BUT this is a FULL university. We do not have a Ph.D. program but have a small master’s program. So have few students for research mentoring. Still some Master students from my home Institute, Drew Shealy, Kirk, Lewis Driskell, and others from COFC did research or independent studies with me. Due to Indian University policies, though I supervised two students: Faruqi received a Ph.D. already and Shinde who is ready to submit, have not listed me as advisors: but written more papers with me than the “official” advisor. I have 5 papers with them. Kasifa Namyalo (Uganda) received her Ph.D. and I am her official advisor. Isa Ndungo (Uganda) Master’s and Dinkayehu and Zebene are still doing their Ph.D. with me from Ethiopia. I also wrote with Fitina (Australia), Mutoh(Japan), and Moolsombut (Thailand) with the blessings from their advisors.

Publications with Undergraduate Students

The following papers are a subset of my list of publications that have been written with my undergraduate students. The challenge for Mathematics with students is asking questions that are appropriately deep, interesting and have the scope for further development. A “net” integration of research helped me a lot: High school student Sarah Malick’s work became the basis of a chapter of Faruqi’s Ph.D. thesis(India). Blaine’s work had seeds from Ndungo (a master’s student), and then it helped a part of Kasifa Namyalo’s ’s Ph.D. thesis (Uganda). Cowden’s project came from Will Bezire’s and helped Dinkayehu’s thesis (Ethiopia). Devin Henson’s work suggested a Ph.D. topic for a student from Auburn. Chaiwoot’s master’s (Thailand) was motivated by Beam’s paper . Aidyn’s paper is the seed for a Ph.D. project of Zebene (Ethiopia) which I co-supervised.

Billings, Blaine*; Namyalo, Kasifa; Sarvate, Dinesh G. EGDD(n1+n2,3;λ1,λ2) for n1=2 and n1=5. Ars Combin. 150 (2020), 281–293.

Sarvate, Dinesh G.; Cowden, William* A simple construction of 3-GDDs with block size 4 using SQS(v). Bull. Inst. Combin. Appl. 84 (2018), 40–44. 05B05

Billings, Blaine*; Namyalo, Kasifa*; Sarvate, Dinesh G. GDD(n1+n2,3;λ1,λ2) with equal number of blocks of two configurations. J. Combin. Math. Combin. Comput. 102 (2017), 19–44.

Chan, Hau*; Hein, Derek W.; Sarvate, Dinesh G. Sarvate-beam designs: new existence results and large sets. J. Combin. Math. Combin. Comput. 83 (2012), 211–216.

Chan, Hau*; Sarvate, Dinesh G. Stanton graph decompositions. Bull. Inst. Combin. Appl. 64 (2012), 21–29.

Chan, Hau*; Sarvate, Dinesh G. On 1-Sarvate-Beam designs. Discrete Math. 311 (2011), no. 10-11, 856–865.

Chan, Hau*; Sarvate, Dinesh G. Beautifully ordered balanced incomplete block designs. J. Combin. Math. Combin. Comput. 74 (2010), 65–81.

Chan, Hau*; Sarvate, Dinesh G. A non-existence result and large sets for Sarvate-Beam designs. Ars Combin. 95 (2010), 193–199.

Chan, Hau*; Sarvate, Dinesh G. Sets of MOLSs generated from a single Latin square. Proceedings of the Fortieth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 195 (2009), 115– 123.

Mishra, Nutan; Sarvate, Dinesh G.; Chisholm, Adrienne*; Raab, Jesse J.* A note on non-regular planar graphs. J. Combin. Math. Combin. Comput. 66 (2008), 17–31.

Sarvate, Dinesh G.; Beam, William* The non-existence of (n−2)- SB(n,n−1) adesigns and some existence results. Bull. Inst. Combin. Appl. 51 (2007), 73–79.

Sarvate, Dinesh G.; Beam, William* A new type of block design. Bull. Inst. Combin. Appl. 50 (2007), 26–28.

Henson, D.*; Sarvate, D. G.; Hurd, S. P. Group divisible designs with three groups and block size four. Discrete Math. 307 (2007), no. 14, 1693–1706.

Henson, Devin*; Sarvate, Dinesh G. A family of group divisible designs of block size four and three groups with λ1=2 and λ2=1 using MOLS. Ars Combin. 78 (2006), 123–125.

Hurd, Spencer P.; Purewal, Tarsem S.*; Sarvate, Dinesh G. Faithful enclosings of group divisible designs formed by adding an additional group. Proceedings of the Thirty-Fourth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 161 (2003), 129–138.

Hurd, Spencer P.; Purewal, Tarsem S.*; Sarvate, Dinesh G. Minimal enclosings of group divisible designs with block size 3 and group size 2. 15th MCCCC (Las Vegas, NV, 2001). J. Combin. Math. Combin. Comput. 46 (2003), 205–225.

Hurd, Spencer P.; Munson, Patrick*; Sarvate, Dinesh G. Minimal enclosings of triple systems. I. Adding one point. Ars Combin. 68 (2003), 145–159.

Sarvate, Dinesh G.; Strehl, Alexander L.* Linear codes through Latin squares modulo n. Bull. Inst. Combin. Appl. 37 (2003), 73–81.

Miller, Kevin C.*; Sarvate, Dinesh G. An application of symmetric chains to a statistical database compromise prevention problem. Bull. Inst. Combin. Appl. 13 (1995), 57–64.

Mirchandani, Jaideep*; Sarvate, Dinesh G. Some necessary existence conditions, constructions, and a list of partially balanced ternary designs. Proceedings of the Twenty-fourth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, FL, 1993). Congr. Numer. 96 (1993), 165–183.

Billings, Blaine GDD(n,2,4;λi,λ2) with equal number of blocks of three configurations. J. Combin. Math. Combin. Comput. 110 (2019), 9–18.

Strehl, Alexander L. Ternary codes through ternary designs. Australas. J. Combin. 30 (2004), 21–29.

Publications with Non-Undergraduate Students

The following papers are a subset of my list of publications that have been written with my non-undergraduate students.

Sarvate, Dinesh G.; Shinde, Pramod N.*; Missing blocks of two designs in Hanani's paper. Bull. Inst. Combin. Appl. 94 (2022), 73–79.

Sarvate, Dinesh G.; Shinde, Pramod N.* A short note on 3-GDDs with 3 groups and block size 4. J. Combin. Math. Combin. Comput. 114 (2020), 329– 339.

Namyalo, Kasifa*; Sarvate, Dinesh G.; Zhang, Li GDD(n1,n,n+1,4;λ1,λ2): n1=1 or 2. J. Combin. Math. Combin. Comput. 110 (2019), 19–37.

Faruqi, Shahab*; Katre, Shashikant A.; Sarvate, Dinesh G. On edge decompositions of a complete graph into smaller complete graphs. J. Combin. Math. Combin. Comput. 106 (2018), 83–107.

Faruqi, Shahab*; Katre, S. A.; Sarvate, Dinesh G. Decomposition of λKv into multigraphs with four vertices and five edges. Ars Combin. 136 (2018), 287– 316.

Ndungo, Issa*; Sarvate, Dinesh G. GDD(n,2,4;λ1,λ2) with equal number of even and odd blocks. Discrete Math. 339 (2016), no. 4, 1344–1354.

Faruqi, Shahab*; Sarvate, Dinesh G. On perfect MRDs. Bull. Inst. Combin. Appl. 78 (2016), 23–40.

Malick, Sarah*; Sarvate, Dinesh G. Decomposition of λKv into multigraphs with four vertices and five edges. J. Combin. Math. Combin. Comput. 86 (2013), 221–237.

Mitchener, Garrett; Sarvate, Dinesh G.; Shealy, Andrew* Further existence results on beautifully ordered balanced incomplete block designs. J. Combin. Math. Combin. Comput. 86 (2013), 151–161.

Hemakul, W.; Moolsombut, C.*; Sarvate, Dinesh G. Restricted simple 1- designs. J. Combin. Math. Combin. Comput. 77 (2011), 217–226.

Sarvate, Dinesh G.; Shealy, Andrew K.* Embedding into complements! Bull. Inst. Combin. Appl. 67 (2013), 73–80.

Fitina, L. F.*; Seberry, Jennifer; Sarvate, Dinesh On F-squares and their critical sets. Australas. J. Combin. 19 (1999), 209–230.

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