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Hunter Snevily

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Hunter Snevily
Born(1956-06-15)June 15, 1956
DiedNovember 11, 2013(2013-11-11) (aged 57).[1]
NationalityAmerican
Alma materEmory University
University of Illinois Urbana-Champaign
OccupationMathematician
EmployerUniversity of Idaho
Known forContributions in Set theory, Graph theory, and Ramsey theory on the integers[2]

Hunter Snevily (1956–2013) was an American mathematician with expertise and contributions in Set theory, Graph theory, Discrete geometry, and Ramsey theory on the integers.[2]

Education and career

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Hunter received his undergraduate degree from Emory University in 1981,[1] and his Ph.D. degree from the University of Illinois Urbana-Champaign under the supervision of Douglas West in 1991.[1][3] After a postdoctoral fellowship at Caltech, where he mentored many students, Hunter took a faculty position at the University of Idaho in 1993 where he was a professor until 2010.[1] He retired early [4] while fighting with Parkinsons,[1][2] but continued research in mathematics till his last days.[1][2]

Mathematics research

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The following are some of Hunter's most important contributions (as discussed in [2]):

  • Hunter formulated a conjecture (1991) [5] bounding the size of a family of sets under intersection constraints. He conjectured that if is a set of positive integers and is a family of subsets of an -set satisfying whenever , then . His conjecture was ambitious in a way it would beautifully unify classical results of Nicolaas Govert de Bruijn and Paul Erdős (1948),[6] Bose (1949),[7] Majumdar (1953),[8] H. J. Ryser (1968),[9] Frankl and Füredi (1981),[10] and Frankl and Wilson (1981).[11] Hunter finally proved his conjecture in 2003[12]
  • Hunter made important contribution to the well known Chvátal's Conjecture (1974)[13] which states that every hereditary family of sets has a largest intersecting subfamily consisting of sets with a common element. Schönheim[14] proved this when the maximal members of have a common element. Vašek Chvátal proved it when there is a linear order on the elements such that implies when for . A family has as a dominant element if substituting for any element of a member of not containing yields another member of . Hunter's 1992 result[15] greatly strengthened both Schönheim's result and Chvátal's result by proving the conjecture for all families having a dominant element; it was major progress on the problem.
  • One of his most cited papers[16] is with Lior Pachter and Bill Voxman[17] on Graph pebbling. This paper and Hunter's later paper[18] with Foster added several conjectures on the subject and together have been cited in more than 50 papers.
  • Hunter made important contributions[19][20][21] on the Snake-in-the-box problem and on the Graceful labeling of graphs.
  • One of Hunter's conjectures (1999)[22] became known as Snevily's Conjecture:[23] Given an abelian group of odd order, and subsets and of , there exists a permutation of such that are distinct. Noga Alon[24] proved this for cyclic groups of prime order. Dasgupta et al. (2001).[25] proved it for all cyclic groups. Finally, after a decade, the conjecture was proved for all groups by a young mathematician Arsovski.[26] Terence Tao devoted a section to Snevily's Conjecture in his well-known book Additive Combinatorics.
  • Hunter collaborated the most[27][28][29][21][30][31][32][33] with his long-term friend[2] André Kézdy. After retirement, he became friends with Tanbir Ahmed[2] and explored experimental mathematics that resulted in several publications [34][35][36][37][38][39]

References

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  1. ^ a b c d e f "Hunter Snevily's obituary in The Moscow-Pullman Daily News". 2013-11-25.
  2. ^ a b c d e f g Ahmed, Tanbir; Kézdy, André; West, Douglas (2015). "Remembering Hunter Snevily". Bulletin of the Institute of Combinatorics and its Applications. 73: 7–17. MR 3331369.
  3. ^ Hunter Snevily at the Mathematics Genealogy Project
  4. ^ "Hunter Snevily retires" (PDF). 2022-10-22.
  5. ^ Snevily, Hunter (1991). "Combinatorics of Finite Sets". University of Illinois Urbana-Champaign.
  6. ^ de Bruijn, Nicolaas G.; Erdős, Paul (1948). "On a Combinatorial Problem". Indagationes Mathematicae. 10: 421–423.
  7. ^ Bose, R. C. (1949). "A note on Fisher's inequality for balanced incomplete block designs". Annals of Mathematical Statistics. 20 (4): 619–620. doi:10.1214/aoms/1177729958.
  8. ^ Majumdar, K. N. (1953). "On some theorems in combinatorics relating to incomplete block designs". Annals of Mathematical Statistics. 24 (3): 377–389. doi:10.1214/aoms/1177728978.
  9. ^ Ryser, H. J. (1968). "An extension of a theorem of de bruijn and Erdős on combinatorial designs". Journal of Algebra. 10 (2): 246–261. doi:10.1016/0021-8693(68)90099-9.
  10. ^ Frankl, P.; Füredi, Zoltán (1981). "Families of finite sets with a missing intersection". Proc. Colloq. Math. Soc. Janos Bolyai (Eger, Hungary). 37: 305–318.
  11. ^ Frankl, P.; Wilson, R. M. (1981). "Intersection theorems with geometric consequences". Combinatorica. 1 (4): 357–368. doi:10.1007/BF02579457. S2CID 6768348.
  12. ^ Snevily, Hunter (2003). "A sharp bound for the number of sets that pairwise intersect at positive values". Combinatorica. 23 (3): 527–533. doi:10.1007/s00493-003-0031-2. S2CID 20035419.
  13. ^ Chvátal, V. (1974). Unsolved Problem No. 7. Hypergraph Seminar (Proc. First Working Sem., Ohio State Univ., Columbus, Ohio, 1972). Lecture Notes in Mathematics. Vol. 411. pp. Springer, Berlin.
  14. ^ Schönheim, J. (1976). "Hereditary systems and Chvátal's conjecture, in: Proceedings of the Fifth British Combinatorial Conference (Univ. Aberdeen, Aberdeen, 1975)". Congressus Numerantium. XV: 537–539.
  15. ^ Snevily, Hunter (1992). "A New Result on Chvátal's Conjecture". Journal of Combinatorial Theory. Series A. 61: 137–141. doi:10.1016/0097-3165(92)90059-4.
  16. ^ "Hunter Snevily". 2022-10-18. in ZbMATH Open
  17. ^ Pachter, Lior; Snevily, Hunter S.; Voxman, Bill (1995). "On pebbling graphs" (PDF). Proceedings of the Twenty-Sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1995). Congressus Numerantium. Vol. 107. pp. 65–80. MR 1369255. Archived from the original (PDF) on 2015-11-25.
  18. ^ Snevily, Hunter; Foster, J. A. (2000). "The 2-pebbling property and a conjecture of Graham's". Graphs and Combinatorics. 16 (2): 231–244. doi:10.1007/PL00021179. S2CID 12095903.
  19. ^ Snevily, Hunter (1994). "The snake-in-the-box problem: A new upper bound". Discrete Mathematics. 133 (1–3): 307–314. doi:10.1016/0012-365X(94)90039-6.
  20. ^ Snevily, Hunter (1997). "New families of graphs that have -labelings". Discrete Mathematics. 170: 185–194. doi:10.1016/0012-365X(95)00159-T.
  21. ^ a b Kézdy, André; Snevily, Hunter (2002). "Distinct sums modulo n and tree embeddings". Combinatorics, Probability and Computing. 11 (1): 35–42. doi:10.1017/S0963548301004874. S2CID 26848303.
  22. ^ Snevily, Hunter (1999). "Unsolved Problems: The Cayley Addition Table of ". American Mathematical Monthly. 106 (6): 584–585.
  23. ^ "Snevily's conjecture". 2022-10-21.
  24. ^ Alon, Noga (2000). "Additive Latin transversals". Israel Journal of Mathematics. 117: 125–130. doi:10.1007/BF02773567. S2CID 16047303.
  25. ^ Dasgupta, S.; Karolyi, Gy.; Serra, O.; Szegedy, B. (2001). "Transversals of additive Latin squares". Israel Journal of Mathematics. 126: 17–28. doi:10.1007/BF02784149. S2CID 17826107.
  26. ^ Arsovski, Bodan (2011). "A proof of Snevily's Conjecture". Israel Journal of Mathematics. 182: 505–508. doi:10.1007/s11856-011-0040-6. S2CID 119529990.
  27. ^ Kézdy, André E.; Snevily, Hunter S.; Wang, Chi (1996). "Partitioning permutations into increasing and decreasing subsequences". Journal of Combinatorial Theory. Series A. 73 (2): 353–359. doi:10.1016/S0097-3165(96)80012-4.
  28. ^ Kézdy, André E.; Snevily, Hunter S. (1997). "On extensions of a conjecture of Gallai". Journal of Combinatorial Theory. Series B. 70 (2): 317–324. doi:10.1006/jctb.1997.1764.
  29. ^ Kézdy, André E.; Nielsen, Mark J.; Snevily, Hunter S. (2001). "Generalized triangle inequalities in ". Bulletin of the Institute of Combinatorics and Its Applications. 33: 23–28.
  30. ^ Kézdy, André E.; Snevily, Hunter S. (2004). "Polynomials that vanish on distinct th roots of unity". Combinatorics, Probability and Computing. 13 (1): 37–59. doi:10.1017/S0963548303005923. S2CID 7061368.
  31. ^ Kézdy, André E.; Snevily, Hunter S.; White, Susan C. (2009). "Generalized Schur numbers for ". Electronic Journal of Combinatorics. 16 (1): R105. doi:10.37236/194.
  32. ^ Jobson, Adam S.; Kézdy, André E.; Snevily, Hunter S.; White, Susan C. (2011). "Ramsey functions for quasi-progressions with large diameter". Journal of Combinatorics. 2 (4): 557–573. doi:10.4310/JOC.2011.v2.n4.a5.
  33. ^ Brauch, Timothy M.; Kézdy, André E.; Snevily, Hunter (2014). "The combinatorial Nullstellensatz and DFT on perfect matchings in bipartite graphs". Ars Combinatoria. 114: 461–475.
  34. ^ Ahmed, Tanbir; Eldredge, Michael; Marler, Jonathan; Snevily, Hunter (2013). "Strict Schur Numbers". Integers. 13: A22. MR 3083484.
  35. ^ Tanbir Ahmed and Hunter Snevily, Bull. Inst. Combin. Appl., 68 (2013), 55-69. (PDF) MR3136863. Ahmed, Tanbir; Snevily, Hunter (2013). "Some properties of Roller Coaster Permutations". Bulletin of the Institute of Combinatorics and its Applications. 68: 55–69. MR 3136863.
  36. ^ Ahmed, Tanbir; Dybizbański, Janusz; Snevily, Hunter (2013). "Unique Sequences Containing No k-Term Arithmetic Progressions". Electronic Journal of Combinatorics. 20 (4): P29. doi:10.37236/3007. MR 3158268.
  37. ^ Ahmed, Tanbir; Snevily, Hunter (2013). "Sparse Distance Sets in the Triangular Lattice". Electronic Journal of Combinatorics. 20 (4): P33. doi:10.37236/3263. MR 3158272.
  38. ^ Ahmed, Tanbir; Snevily, Hunter (2014). "The -labeling number of comets is ". Bulletin of the Institute of Combinatorics and its Applications. 72: 25–40. MR 3362514.
  39. ^ Ahmed, Tanbir; Kullmann, Oliver; Snevily, Hunter (2014). "On the van der Waerden numbers ". Discrete Applied Mathematics. 174: 27–51. arXiv:1102.5433. doi:10.1016/j.dam.2014.05.007. MR 3215454. S2CID 290091.