Jeff Dinitz

Jeff Dinitz Curriculum Vitae

Institution: Dept. of Mathematics and Statistics, University of Vermont
email: Jeff.Dinitz(at)uvm.edu
Home Page URL: https://site.uvm.edu/jdinitz/?page_id=5

Educational Background

  • B.S., 1974, Mathematics, Carnegie-Mellon University
  • M.S., 1976, Mathematics, The Ohio State University
  • Ph.D., 1980, Mathematics, The Ohio State University. Thesis Advisor: R. M. Wilson

Employment

  • Teaching Associate, Mathematics, 1974 — 1980, The Ohio State University
  • Assistant Professor, Mathematics and Statistics, 1980 — 1985, University of Vermont
  • Associate Professor, Mathematics and Statistics, 1985 — 1992, University of Vermont
  • Associate Department Chair, Mathematics and Statistics, 1989 — 1993, University of Vermont
  • Professor, Mathematics and Statistics, 1992 — Present, University of Vermont
  • Professor (Secondary Appointment), Computer Science and Electrical Engineering, 1994 — 2000 University of Vermont
  • Professor (Secondary Appointment), Computer Science, 2001 — Present, University of Vermont
  • Department Chair, Mathematics and Statistics, 1998 — 2004, University of Vermont
  • Interim Department Chair, Computer Science, 2010 — 2012, University of Vermont
  • Acting Associate Chair, Mathematics, 2016 — 2017, University of Vermont.
  • Williams Professor of Mathematics, 2016 – 2019, University of Vermont.
  • Emeritus Professor of Mathematics and Statistics, 2019 – present, Universty of Vermont

Visiting Positions

  • The Ohio State University, January – May, 1988
  • Institute for Mathematics and its Applications, Minneapolis, Minnesota, June 1988.
  • The University of Queensland (Australia), April 2014

Honors and Awards

  • University Scholar, 2008-2009, University of Vermont. (Four university-wide awards per year)
  • Ethel Raybould Visiting Fellowship, School of Mathematics and Physics, University of Queensland, 2014
  • Outstanding Faculty Performance, College of Engineering and Mathematics, University of Vermont, 2015. (One college-wide award per year).
  • Williams Professor of Mathematics, 2016 — present, University of Vermont. (The oldest named professorship at UVM).

Books and Edited Volumes

  • Contemporary Design Theory: A Collection of Surveys, edited with D.R. Stinson, John Wiley and Sons, Inc., 1992. ISBN 0-471-53141-3
  • Coding Theory, Design Theory, Group Theory: Proceedings of the Marshall Hall Conference, edited with D. Jungnickel, S.A. Vanstone, K.T. Arasu, M. Ashbacher, and R. Foote, John Wiley and Sons, Inc., 1993. ISBN 0-471-55703-X
  • CRC Handbook of Combinatorial Designs, edited with C.J. Colbourn, CRC Press, 1996. ISBN 0-8493-8948-8
  • Discrete Math. Vol. 261 (#1-3) (2003), 1-462, edited with C. J. Colbourn and D. Froncek. This volume contains 30 papers honoring the occasion of the 65th birthday of Alex Rosa.
  • The Handbook of Combinatorial Designs (Second Edition), edited with C.J. Colbourn, Chapman & Hall/CRC, 2006. ISBN 1-5848-8506-8
  • Discrete Math. 309 (#3) (2009), 513-614, edited with H. Kharaghani, G.B. Khosrovshahi and S. Shahriari. This volume contains papers presented at the International Workshop on Design Theory, Graph Theory, and Computational Methods – IPM Combinatorics II, in Tehran, Iran in April 2006.
  • Australasian J. of Combinatorics, Vol 67, Part 2 (2017), 65-393. Edited with Paul Bonnington and Jozef Širáň. This volume contains 21 research papers in memory of Dan Archdeacon.

Refereed Publications

  1. New lower bounds for the number of pairwise orthogonal symmetric Latin squares, Congressus Numerantium 23 (1979), pp. 393-398.
  2. Boss block designs (with D.R. Stinson), Ars Combinatoria 9 (1980), pp. 59-68.
  3. A fast algorithm for finding strong starters (with D.R. Stinson), SIAM J. on Algebraic and Discrete Methods, Vol. 2, No. 1, March 1981, pp. 50-56.
  4. Some new row complete Latin squares (with D. Archdeacon, D.R. Stinson, and T. W. Tillson), Journal of Combinatorial Theory (A), Vol. 29, No. 3, Nov. 1980, pp. 393-398.
  5. The construction and uses of frames (with D.R. Stinson), Ars Combinatoria 10 (1980), pp. 31-53.
  6. A note on Howell designs of odd side (with D.R. Stinson), Utilitas Mathematics 18 (1980), pp. 207-216.
  7. Further results on frames (with D.R. Stinson), Ars Combinatoria 11 (1981), pp. 275-288.
  8. The spectrum of Room cubes (with D.R. Stinson), European Journal of Combinatorics 2 (1981), pp. 221-230.
  9. Pairwise orthogonal symmetric latin squares, Congressus Numerantium 32 (1981), pp. 261-265.
  10. The existence of certain Room graphs, Ars Combinatoria 13 (1982), pp. 115-128.
  11. Continuous maps in block designs (with S.W. Margolis), Ars Combinatoria 14 (1982), pp. 21-45.
  12. Continuous maps in finite projective space (with S.W. Margolis), Congressus Numerantium 35 (1982), pp. 239-244.
  13. Translational hulls and block designs (with S.W. Margolis), Semigroup Forum 27 (1983), pp. 247-263.
  14. MOLS with holes (with D.R. Stinson), Discrete Math 44 (1983), pp. 145-154.
  15. On nonisomorphic Room squares (with D.R. Stinson), Proceedings of American Math Soc., Vol. 89, No. 1, Sept. 1983, pp. 175-181.
  16. Room n-cubes of low order, J. Austral. Math Soc. (Series A) 36 (1984), pp. 237-252.
  17. Room squares with holes of side 3, 5 and 7 (with D.R. Stinson and W.D. Wallis), Discrete Math 47 (1983), pp. 221-228.
  18. Four orthogonal one-factorizations on ten points (with W.D. Wallis), Annals of Discrete Math 26 1985, pp. 143-150.
  19. Orthogonal one-factorization graphs, Journal of Graph Theory 9 (1985), pp. 147-159.
  20. Sets of orthogonal one-factorizations of K10 (with D.S. Archdeacon and W.D. Wallis), Congressus Numerantium 43 (1984) pp. 45-79.
  21. V-squares (with D.S. Archdeacon and D.R. Stinson), Ars Combinatoria 19 (1985), pp. 161-174.
  22. Orthogonal edge colorings of graphs (with D.S. Archdeacon and F. Harary), Congressus Numerantium 47 (1985) pp. 49-67.
  23. A hill-climbing algorithm for one-factorizations and Room squares (with D.R. Stinson), SIAM J. Algebraic and Disc. Methods, Vol. 8, No. 3 (1987), pp. 430-438.
  24. The existence of Room 5-cubes, Journal of Combinatorial Theory (A), Vol. 45, No. 1 (1987), pp. 125-138.
  25. Factorizations and orthogonal matchings (with D.S. Archdeacon), Congressus Numerantium 58 (1987), pp. 69-74.
  26. Some perfect Room squares, Journal of Combinatorial Mathematics and Combinatorial Computing 2 (1987), pp. 29-36.
  27. On the existence of Room squares with subsquares (with D.R. Stinson), Contemporary Mathematics 111 (1990), pp.73-91.
  28. Some new perfect 1-factorizations from starters in finite fields (with D.R. Stinson), Journal of Graph Theory 13 (1989), pp. 405-415.
  29. Constructing indecomposable 1-factorizations of the complete multigraph (with D.S. Archdeacon), Discrete Math 92 (1991), pp. 9-19.
  30. Orthogonal 1-factorizations of the complete multigraph, Coding Theory and Design Theory, Part II, IMA Vol. in Math. and its Applications, Vol. 21, Springer, New York – Berlin (1990), pp. 70-85.
  31. Spanning sets and scattering sets in Steiner triple systems (with C.J. Colbourn and D.R. Stinson), Journal of Combinatorial Theory (A) 57 (1991), pp. 46-59.
  32. Indecomposable triple systems with lambda = 6, Journal of Combinatorial Mathematics and Combinatorial Computing 5 (1989), pp. 139-142.
  33. Heuristic algorithms for finding irregularity strengths of graphs (with D.K. Garnick), Journal of Combinatorial Mathematics and Combinatorial Computing 8 (1990), pp. 195-208.
  34. Trains: an invariant for one-factorizations (with W.D. Wallis), Ars Combinatoria 32 (1991), pp. 161-180.
  35. Indecomposable triple systems exist for all lambda (with D. Archdeacon), Discrete Math 113 (1993), pp. 1-6.
  36. A brief introduction to design theory (with D.R. Stinson), Contemporary Design Theory: A Collection of Surveys, Wiley, New York, 1992, pp. 1-12.
  37. Room squares and related designs (with D.R. Stinson), Contemporary Design Theory: A Collection of Surveys, Wiley, New York, 1992, pp. 137-194.
  38. The irregularity strength of the m x n grid (with D. K. Garnick and A. Gyarfas), Journal of Graph Theory 16 (1992), pp. 355-374.
  39. A few more Room frames (with D.R. Stinson), Graphs, Matrices and Designs, Marcel Dekker, New York, 1993, pp. 133-146.
  40. Uniform Room frames with five holes (with E.R. Lamken), Journal of Combinatorial Designs 1 (1993), pp. 323-328.
  41. On the number of one-factorizations of the complete graph on 12 points (with D. K. Garnick), Congressus Numerantium, 94 (1993), pp. 159-168.
  42. Howell designs with sub-designs (with E.R. Lamken), Journal of Combinatorial Theory (A) 65 (1994), pp. 268 – 301.
  43. The stipulation polynomial of a uniquely list-colorable graph (with W.J. Martin), Australasian Journal of Combinatorics, 11 (1995), pp. 105 – 115.
  44. Holey factorizations (with D. K. Garnick), Ars Combinatoria, 44 (1996), pp. 65 – 92.
  45. There are 526,915,620 nonisomorphic one-factorizations of K12, (with D.K. Garnick and B.D. McKay), Journal of Combinatorial Designs 2 (1994), pp. 273 – 285.
  46. Thwarts in transversal designs (with C.J. Colbourn and M. Wotjas), Designs, Codes and Cryptography, 5 (1995), pp. 189 – 197.
  47. On the spectra of certain classes of Room frames (with D.R. Stinson and L.Zhu), Electronic Journal of Combinatorics 1 (1994), #R7, 21 pages.
  48. There are 23 nonisomorphic perfect one-factorizations of K14, (with D.K. Garnick), Journal of Combinatorial Designs, 4 (1996), pp. 1-4.
  49. Making the MOLS Table (with C.J. Colbourn), Computational and Constructive Design Theory, (W.D. Wallis, ed.) Kluwer Academic Publishers, Norwell, Ma, 1996, pp. 67-134.
  50. More thwarts in transversal designs (with C.J. Colbourn and D.R. Stinson), Finite Fields and Applications, 2 (1996), pp. 293-303.
  51. Disjoint difference families with block size 3 (with P. Rodney), Utilitas Math., 52 (1997), pp. 153-160
  52. HOPS and COPS in Room frames (with E.R. Lamken), Designs, Codes and Cryptography, 19 (2000), pp. 5-26.
  53. N(n) and nu(n): similarities and differences (with C.J. Colbourn), in Combinatorics, Complexity and Logic (D.S. Bridges et al, eds.), Springer, Berlin, 1996, pp. 25-36.
  54. Complete arcs in Steiner triple systems (with C.J. Colbourn), Journal of Combinatorial Theory (A), 80 (1997), pp. 320-333
  55. Room square patterns (with E.R. Lamken), Journal of Statistical Planning and Inference, 86 (2000), pp. 397-410.
  56. Generating sets in Steiner triple systems, (with C.J. Colbourn), Mathematica Slovaca, 50 (2000), pp. 259-269.
  57. Quorum systems constructed from Combinatorial Designs, (with C.J. Colbourn and D.R. Stinson), Information and Comutation, 169 (2001), 160-173.
  58. Block disjoint difference families for Steiner triple systems: v = 3 mod 6, (with Nabil Shalaby), Journal of Statistical Planning and Inference, 106 (2002), 77-86.
  59. Bicoloring Steiner triple systems, (with C.J. Colbourn and A. Rosa), Electronic Journal of Combinatorics , 6 (1999), #R25, 16 pages.
  60. Selected applications of combinatorial design theory, (with C.J. Colbourn and D.R. Stinson), Surveys in Combinatorics, 1999 , (J.D Lamb and D.A. Preece, eds), Cambridge Univ. Press, Cambridge, pp. 37 – 100.
  61. Mutually orthogonal latin squares: A brief survey of constructions, (with C.J. Colbourn), Journal of Statistical Planning and Inference, 95 (2001), pp 9-48.
  62. The existence of referee squares, (with A.C.H. Ling), Discrete Mathematics, 232 (2001), 109 – 112.
  63. Combinatorics in undergraduate courses, (with I. Anderson, C. Rodger, and B. Webb), Bulletin of the Institute for Combinatorics and its Applications, 32 (2001), 37 – 52..
  64. Scheduling the XFL, (with D. Froncek), Congressus Numerantium, 147 (2000), 5 – 15
  65. A singular direct product for bicoloring Steiner triple systems (with D.R. Stinson), Codes and Designs (edited by K.T. Arasu and A. Seress), de Gruyter, Berlin, 2002, 87 – 98.
  66. Complementary partial resolution squares for Steiner triple systems (with E.R. Lamken and A.C.H. Ling), Discrete Math, 261 (2003), 243-254.
  67. New lower bounds on the maximum number of mutually orthogonal Steiner triple systems (with P. Dukes), Designs 2002: Further Computational and Constructive Design Theory, (W.D. Wallis, ed.) Kluwer Publishers, Norwell, Ma, 2002, 81 – 101.
  68. Sets of three pairwise orthogonal Steiner triple systems, (with A.C.H. Ling and P. Dukes), Journal of Combinatorial Theory (A), 101 (2003), 90 – 116.
  69. Cycle systems in the complete bipartite graph minus a one-factor (with D. Archdeacon, M. Debowsky and H. Gavlas), Discrete Math. , 284 (2004) (Special issue in honor of Curt Lindner on his 65th birthday), 37-43. http://authors.elsevier.com/sd/article/S0012365X04001207
  70. Enumeration of balanced tournament designs on 10 points (with M. Dinitz), Journal of Combinatorial Mathematics and Combinatorial Computing, 52 (2005), 51 – 64.
  71. On the maximum number of different ordered pairs of symbols in sets of latin squares (with D. R. Stinson), Journal of Combinatorial Designs, 13 (2005), 1- 15.
  72. On assigning referees to tournament schedules (with D.R. Stinson), Bulletin of the Institute of Combinatorics and its Applications, 44 (2005), 22 – 28.
  73. Sequentially perfect and uniform one-factorizations of the complete graph (with P. Dukes and D.R. Stinson), Electron. J. Combin. 12 (2005), #R1, 12 pages.
  74. Designing schedules for leagues and tournaments, Graph Theory Notes of New York, 48 (2005), 7 – 21.
  75. On the structure of uniform one-factorizations from starters in finite fields (with P. Dukes), Finite Fields and Applications, 12 (2006), 283 – 300.
  76. Fault Tolerant Routings with Minimum Optical Index (with A.C.H. Ling and D.R. Stinson), Networks, 48 (2006), 47-55.
  77. Perfect hash families from transversal designs (with A.C.H. Ling and D.R. Stinson), Australasian Journal of Combinatorics, 37 (2007), 233-242.
  78. Two new infinite families of extremal class-uniformly resolvable designs (with A.C.H. Ling), Journal of Combinatorial Designs, 16 (2008), 213-220.
  79. Maximum uniformly resolvable designs with block sizes 2 and 4 (with A.C.H. Ling and P. Danziger), Discrete Math 309 (2009), pp. 4716-4721, Special issue in honor of Anthony Hilton.
  80. The Hamilton-Waterloo problem: The case of triangle-factors and one Hamilton cycle (with A.C.H. Ling), Journal of Combinatorial Designs, 17 (2009), 160-176.
  81. The Hamilton-Waterloo problem with triangle-factors and Hamilton cycles: The case n = 3 (mod 18) (with A.C.H. Ling). Journal of Combinatorial Mathematics and Combinatorial Computing, 70 (2009), 143 — 147.
  82. On Hamiltonian paths with prescribed edge lengths in the complete graph (with S. Janiszewski), Bulletin of the Institute of Combinatorics and its Applications, 57 (2009), 42–52.
  83. On orthogonal generalized equitable rectangles (with H. Cao, D. Kreher, D. Stinson, R. Wei), Des. Codes Cryptogr. 51 (2009), 225–230.
  84. The existence of N2 resolvable latin squares (with A.J. Wolfe and A.C.H. Ling), SIAM J. Discrete Math., 23 (2009), 1217–1237.
  85. The spectra of certain classes of Room frames: The last cases (with G. Warrington), Electron. J. Combin 17 (2010), #R74, 13 pages.
  86. Constructions for retransmission permutation arrays (with M.B. Patterson, D.R. Stinson and R. Wei), Des. Codes Cryptogr. , 65 (2012), 325 — 351.
  87. Packing Costas Arrays (with P.J.R. Ostergard and D. R. Stinson), Journal of Combinatorial Mathematics and Combinatorial Computing, 80 (2012), 385–403.
  88. Estimating landscape carrying capacity through maximum clique analysis (with T.M. Donovan, G. Warrington and W.S. Schwenk), Ecological Applications, 22 (2012), 2265 — 2276.
  89. On the existence of three dimensional Room frames and Howell cubes (With E.R. Lamken and G.S. Warrington) Discrete Mathematics, 313 (2013) 1368 — 1384.
  90. An analysis of NK landscapes: Interaction structure, statistical properties and expected number of local optima (with J. Buzas) IEEE Transactions on Evolutionary Computing, 18 (2014), 807 — 818.
  91. On Maximal Partial Costas Latin Squares (with M.R. Frank) Journal of Combinatorial Mathematics and Combinatorial Computing, 93 (2015), 23-32
  92. Square integer Heffter arrays with empty cells (with D.S. Archdeacon, D.M. Donovan, and E. S. Yazici), Des. Codes Cryptogr., 77 (2015), 409 — 426
  93. On Partial Sums in Cyclic Groups (with D.S. Archdeacon, A. Mattern and D.R. Stinson), Journal of Combinatorial Mathematics and Comb. Computing, 98 (2016), 327-342.
  94. Guest Editorial: Special issue in honour of Dan S. Archdeacon, (with P. Bonnington and J. Širáň), Australasian Journal of Combinatorics, 67 (2017), 65 – 76.
  95. Biembedding Steiner triple systems and n-cycle systems on orientable surfaces (with A. Mattern), Australasian Journal of Combinatorics, 67 (2017), 327 -344.
  96. Tight Heffter arrays exist for all possible orders, (with D.S. Archdeacon and T. Boothby). J. of Combinatorial Designs 25 (2017), 5 – 35.
  97. The existence of square integer Heffter arrays, (with I.M. Wanless), Ars. Math. Contemp. 13 (2017), 81 — 93.
  98. The existence of square non-integer Heffter arrays (with N.J. Cavenaugh, D. Donovan and E. S. Yazici), Ars. Math. Contemp, 17 (2019), 369 – 395.
  99. Seeds for generalized taxicab numbers (with R. Games and R. Roth), J. Integer Seq. 22 (2019), Article 19.3.3, 16 pages.

Conferences Organized

  • First Vermont Summer Workshop on Combinatorics, with D. Archdeacon, June 1987, 14 participants, budget $3000.
  • Second Vermont Summer Workshop on Combinatorics and Graph Theory, with D. Archdeacon, July 1988, 19 participants, budget $5200.
  • Third Vermont Summer Workshop on Combinatorics and Graph Theory, with D. Archdeacon, June 1989, 30 participants, budget $6800.
  • Fourth Vermont Summer Workshop on Combinatorics and Graph Theory, with D. Archdeacon, June 1990, 30 participants, budget $5400.
  • The Marshall Hall Conference on Coding Theory, Design Theory and Group Theory; with K.T. Arasu, M. Ashbacher, R. Foote, D. Jungnickel, and S. Vanstone; September, 1990; 190 participants; budget $53,000. (Foote and I did all the work).
  • Fifth Vermont Summer Workshop on Combinatorics and Graph Theory, with D. Archdeacon, June 1991, 25 participants, budget $4200.
  • Sixth Vermont Summer Workshop on Combinatorics and Graph Theory, with D. Archdeacon, June 1994, 50 participants, budget $12,000.
  • Emerging Applications of Combinatorial Designs, a workshop at Mathematical Sciences Research Institute, Berkeley, CA, with C. Colbourn and E.R. Lamken. Nov. 2000, 50 participants, budget $30,000
  • WilsonFest: a conference at Caltech honoring the work of Professor Rick Wilson, with P. Dukes, E. Lamken and Q. Zhang, March 2012, 65 participants, budget $40,000. Sponsors: National Security Agency and Caltech.

Other Professional Activities

Professional Organizations:

American Mathematical Society , Institute for Combinatorics and its Applications — Foundation Fellow and member of the Executive Council 1993-1996 and 2018-present

Editorial Boards:

Journal of Combinatorial Designs — Managing Editor-in-Chief (1997-2018).

The CRC Handbook of Combinatorial Designs — co Editor-in-Chief.

Director:

Governor’s Institute for Mathematical Sciences (2004-2014)

Advisory Boards:

International Advisory Board, Centre for Discrete Mathematics and Theoretical Computer Science, University of Auckland and the University of Waikato, New Zealand (1995 – present). Vermont Mathematics Partnership (2004 – 2008)

Referee for:

Journal of Combinatorial Theory (Series A), Ars Combinatoria, Discrete Mathematics, Journal of Combinatorial Mathematics and Combinatorial Computing, Utilitas Mathematica, Annals of Discrete Mathematics, Journal of Combinatorial Designs, Australasian Journal of Combinatorics, Designs, Codes and Cryptography, Congressus Numerantium, Journal of Statistical Planning and Inference, Mathematica SLOVAKA, Zentralblatt fur Mathematics, Math. Reviews, Journal of Combinatorics, Information & System Sciences.

Grant proposal reviewer for:

NSF, Algebra and Number Theory Program; NSA, Mathematical Sciences Program; NSERC, Mathematics Section; State of Lousisiana EPSCoR; National Science Centre (Poland).

External Ph.D Examiner:

University of Toronto; University of Waterloo; University of Rostock, Germany; Helsinki University of Technology; University College, Dublin Ireland; University of Ottawa; University of Queensland, Australia; Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV) (Mexico).

Manuscript reviewer for:

Marcel Dekker, Prentice Hall, John Wiley and Sons, Brooks/Cole.

External Teaching:

Vermont Mathematics Partnership (I designed and taught a math class to in-service high school teachers) 2005, 2006; Mathpath (math camp for gifted middle school students) 2008; Governor’s Institute of Vermont, 2004–present .

Featured TV and Radio Appearances:

Vermont Edition, Vermont Public Radio, 9/12/07; Across the Fence, WCAX TV, 6/9/08

Other:

Constructed schedule of play for the 2001 season of the XFL (football league), with Dalibor Froncek.

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