Publication List

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Journal articles

1. Product formulas for q-Hahn polynomials, SIAM J. Math. Anal. 11 (1980), 100-107.

2. Some q-Krawtchouk polynomials on Chevalley groups, Amer. J. Math. 102 (1980), 625-662.

3. A short proof of a generating function for Jacobi polynomials, Proc. AMS 80 (1980), 398-400.

4. Some Erdös-Ko-Rado theorems for Chevalley groups, SIAM J. Alg. Disc. Meth. 1 (1980), 160-163.

5. Three addition theorems for some q-Krawtchouk polynomials, Geom. Ded. 10 (1981), 403-425.

6. A partially ordered set and q-Krawtchouk polynomials, J. Comb. Th. A 30 (1981), 276-284.

7. Strange evaluations of hypergeometric series (with I. Gessel), SIAM J. Math. Anal. 13 (1982), 295-308.

8. Coefficients in expansions of certain rational functions (with R. Evans and M. Ismail), Can. J. Math. 34 (1982), 1011-1024.

9. Generalized n-gons and Chebychev polynomials, J. Comb. Th. A 34 (1983), 15-27.

10. Applications of q-Lagrange inversion to basic hypergeometric series (with I. Gessel), Trans. AMS 277 (1983), 173-202.

11. An upper bound for the cardinality of an s-distance subset in real Euclidean space (with E. Bannai and E. Bannai), Combinatorica 3 (1983), 147-152.

12. Group actions on Stanley-Reisner rings and invariants of permutation groups (with A. Garsia), Adv. in Math. 51 (1984), 107-201.

13. Asymptotic formulas for zero-balanced hypergeometric series (with R. Evans), SIAM J. Math. Anal. 15 (1984), 1010-1020.

14. Modularly complemented lattices and shellability (with M. Wachs), Cont. Math. 34 (1984), 197-206.

15. Short proofs of Saalsch\"utz's and Dixon's theorems (with I. Gessel), J. Comb. Th. A 38 (1985), 87-90.

16. A Schensted algorithm for rim-hook tableaux (with D. White), J. Comb. Th. A 40 (1985), 211-247.

17. Harmonics on posets, J. Comb. Th. A 40 (1985), 136-149.

18. Another infinite family of q-Lagrange inversion formulas (with I. Gessel), Rocky Mountain J. Math. 16 (1986), 373-384.

19. The triplication formula for Gauss sums (with J. Greene), Aequationes Math. 30 (1986), 134-141.

20. A character sum evaluation and Gaussian hypergeometric series (with J. Greene), J. Number Th. 23 (1986), 136-148.

21. Sign variations of the Macdonald identities, SIAM J. Math. Anal. 17 (1986), 1454-1460.

22. The combinatorics of the q-Hermite polynomials and the Askey-Wilson integral (with M. Ismail and G. Viennot), Eur. J. Comb. 8 (1987), 379-392.

23. On the Askey-Wilson and Rogers polynomials (with M. Ismail), Can. J. Math. 40 (1988), 1025-1045.

24. Association schemes and quadratic transformations for orthogonal polynomials (with L. Chihara), Graphs and Combinatorics 2 (1986), 101-112.

25. t-designs in classical association schemes, Graphs and Combinatorics 2 (1986), 283-286.

26. Bijective proofs of basic hypergeometric series identities (with J. Joichi), Pac. J. Math. 127 (1987), 103-120.

27. An involution for Jacobi's identity (with J. Joichi), Discrete Math., 73 (1989), 261-271.

28. Zeros of generalized Krawtchouk polynomials (with L. Chihara), J. Approx. Th. 60 (1990), 43-57. pdf

29. Unimodality and Young's lattice, J. Comb. Th. A 54 (1990), 41-53. pdf

30. The combinatorics of the z^{AB} theorem (with D. White), Disc. Math. 83 (1990), 105-114.pdf

31. The Odlyzko conjecture and O'Hara's unimodality proof (with D. Zeilberger), Proc. AMS 107 (1989), 39-43. pdf

32. More zeros of Krawtchouk polynomials (with L. Habsieger), Graphs and Combinatorics 9 (1993), 163-172. pdf

33. Sieved partition functions and q-binomial coefficients (with F. Garvan), Math. Comp. 55 (1990), 299-311. pdf

34. Cranks and t-cores (with F. Garvan and D. Kim), Inv. Math. 101 (1990), 1-17. pdf

35. A unimodality identity for Schur functions (with F. Goodman and K. O'Hara), J. Comb. Th. A 60 (1992), 143-146. pdf

36. An algorithmic involution for p(n) (with J. Joichi), J. Algorithms 15 (1993), 223-228. pdf

37. Specializations of generalized Laguerre polynomials (with R. Simion), SIAM J. Math. Anal. 25 (1994), 712-719. pdf

38. The combinatorics of q-Charlier polynomials (with A. de Medicis and D. White), J. Comb. Th. A, 69 (1995), 87-114. pdf

39. Octabasic Laguerre polynomials and permutation statistics (with R. Simion), J. Comp. Appl. Math. 68 (1996), p. 297-329. pdf

40. More monotonicity theorems for partitions (with J. Friedman and J. Joichi), Experimental Math. 3 (1994), 31-37. pdf

41. A matrix equation for association schemes (with L. Chihara), Graphs and Combinatorics 11 (1995), 103-108. pdf

42. Combinatorial orthogonal expansions (with A. de Medicis), PAMS, 124 (1996), 469-473. pdf

43. Classical orthogonal polynomials as moments (with M. Ismail), Can. J. Math. 49 (1997), 520-542.pdf

44. Unimodality of differences of specialized Schur functions (with V. Reiner), J. Alg. Comb.7 (1998), 91-107. pdf

45. Rim hook lattices (with S. Fomin), St. Petersburg Math. J. 9 (1998), 1007-1016. pdf

46. Determinants in plane partition enumeration (with G. Andrews), Eur. J. Comb 19 (1998), 273-282. pdf

47. A hypergeometric hierarchy for the Andrews evaluations, Ramanujan J. 4 (1998), 499-509. pdf

48. Lattice paths and positive trigonometric sums (with M. Ismail and D. Kim), Const. Approx. 15 (1999), 69-81. pdf

49. Quadratic q-exponentials and connection coefficient problems (with M. Ismail and M. Rahman), PAMS 127 (1999), 2931-2941. pdf

50. A convolution formula for the Tutte polynomial (with W. Kook and V. Reiner), J. Comb. Th. B 76 (1999), 297-300. pdf

51. Addition theorems for the q-exponential function (with M. Ismail), Cont. Math. 254 (2000), 235-245. pdf

52. Combinatorial Laplacians of matroid complexes (with W. Kook and V. Reiner), J. AMS 13 (1999), 129-148. pdf

53. Regular realizations of abstract polyhedra of types {3,6} and {6,3} (with H. Burgiel), J. Disc. Comp. Geom. 24 (2000), 241-255. pdf

54. Simultaneous maj statistics (with D. Kim), Sem. Loth. Comb. 42 B42g (1999), 12 pp. pdf

55. Variants of the Rogers-Ramanujan identities (with T. Garrett and M. Ismail), Adv. Appl Math. 23 (1999), 274-299. pdf

56. Change of base in Bailey pairs (with D. Bressoud and M. Ismail), Ramanujan J. 4 (2000), 435-453. pdf

57. Open positivity conjectures for integer partitions, Trends in Mathematics 2 (1999), 19-25 (electronic). dvi Here is the journal pdf

58. Schur's Determinants and Partition Theorems (with M. Ismail and H. Prodinger), Sem. Loth. Comb. 44 B44a, (2000) 10 pp. pdf

59. q-Integral and Moment Representations for q-Orthogonal Polynomials (with Mourad Ismail), Can. J. Math. 54 (2002), 701-735. pdf

60. The Bailey-Rogers-Ramanujan group, Cont. Math. 291 (2001), 55-70. pdf

61. Applications of q-Taylor theorems (with Mourad Ismail), J. Comput. Appl. Math. 153 (2003), no. 1-2, 259-272. pdf

62. Tribasic integrals and identities of Rogers-Ramanujan type (with Mourad Ismail), TAMS, Trans. Amer. Math. Soc. 355 (2003), no. 10, 4061-4091 , pdf

63. Proof of a monotonicity conjecture (with Thomas Prellberg), JCT A, 103 (2003), 377-381, pdf

64. q-Taylor theorems, polynomial expansions, and interpolation of entire functions (with Mourad Ismail), J. Approx. Th., 123 (2003), 125-146. pdf

65. Some positive sums, J. Comp. Appl. Math. 153 (2003), p. 537.

66. The cyclic sieving phenomenon (with V. Reiner and D. White), JCT A 108 (2004), 17-50. pdf

67. The Charney-Davis quantity for certain graded posets (with V. Reiner and V. Welker), Sem. Lothar. Combin. 50 2003-2004.pdf

68. Springer's regular elements over arbitrary fields (with V. Reiner and P. Webb), Math. Proc. Cambridge Philos. Soc. 141 (2006), no. 2, 209--229. pdf

69. Ramanujan Continued Fractions Via Orthogonal Polynomials (with M. Ismail), Adv. Math. 203 (2006), 170-193. pdf

70. The Combinatorics of the Al-Salam-Chihara q-Charlier Polynomials (with D. Kim and J. Zeng), Sem. Loth. Comb. 42 B54i (2006).

71. Block inclusions and cores of partitions (with B. Olsson), Aequat. Math. 74 (2007), 90-110. pdf

72. Bimahonian distributions (with H. Barcelo and V. Reiner) J. Lon. Math. Soc. (2) 77 (2008), 627-646. pdf

73. q-analogues of Euler's Odd=Distinct Theorem, Ramanujan J. 19 (2009), 107-113, pdf

74. The combinatorics of Al-Salam-Chihara q-Laguerre polynomials (with A. Kasraoui and J. Zeng), Adv. Appl. Math 47 (2011), 216-239. pdf

75. (q,t)-analogues and GL_n(F_q) (with V. Reiner), J. Alg. Comb.31 (2010), 411-454. pdf

76. Some combinatorial and analytical identities (with M. Ismail), Ann. of Combinatorics 16 (2012), 755-771. pdf

77. Formulae for Askey-Wilson moments and enumeration of staircase tableaux (with S. Corteel, R. Stanley, and L. Williams, TAMS 364 (2012), 6009-6037. pdf

78. The negative q-binomial (with S. Fu, V. Reiner, and N. Thiem), Elec. J. Comb. 19 (2012), P36. pdf

79. Note on 1-crossing partitions, (with M. Bergerson, A. Miller, A. Pliml, V. Reiner, P. Shearer, and N. Switala) Ars Comb. 99 (2011), 83-97. pdf

80. Orthogonal Basic Hypergeometric Laurent Polynomials, (with M. Ismail), SIGMA 8 (2012), 092, 20 pages. pdf

81. Moments of Askey-Wilson polynomials, (with Jang Soo Kim) JCT A, 125 (2014), 113-145. pdf

82. Reflection factorizations for Singer cycles (with Joel Lewis and Vic Reiner), JACO 40 (2014), 663-691. pdf

83. What is cyclic sieving? (with V. Reiner and D. White), Notices AMS, 61 (2014), 169-171. pdf

84. The q=-1 phenomenon via homology concentration (with P. Hersh and J. Shareshian), J. Comb. 5 (2014), 167-194. pdf

85. Bootstrapping and Askey-Wilson polynomials (with Jang Soo Kim), J. Math. Anal. Appl., 421 (1) (2015), p. 501-520. pdf

86. The combinatorics of associated Laguerre polynomials (with Jang Soo Kim), SIGMA 11 (2015), 039, 12 pages. pdf

87. Expansions in Askey-Wilson polynomials, (with Mourad Ismail), J. Math. Anal. Appl. 424 (2015), no. 1, 664-674. pdf

88. Refinements of the Rogers-Ramanujan identities (with Kathy O'Hara), Exper. Math. 24 (2015), 410-418. pdf

89. On the distribution of the number of fixed vectors for the finite classical groups (with Jason Fulman), Annals of Combinatorics 20 (2016), p. 755-773. pdf

90. Invariants of GL_n(F_q) in polynomials mod Frobenius powers, (with Joel Lewis and Victor Reiner), Proc. R. Soc. Edinburgh A 147 (2017), p. 831-873. pdf

91. On q-integrals over order polytopes (with Jang Soo Kim), Adv. Math. 308 (2017), p. 1269-1317. pdf

92. Asymptotics of the number of involutions in finite classical groups (with Jason Fulman and Robert Guralnick), J. Group Th 20 (2017), p. 871-902. pdf

93. Orthogonality of very well-poised series (with M. Ismail and E. Rains) IMRN to appear, pdf

94. Orthogonal polynomials and Smith normal form (with A. Miller), Mon. Math., to appear, pdf

Conference Proceedings

1. Orthogonal polynomials and Chevalley groups, Special Functions: Group Theoretic Aspects and Applications, ed. by Askey, Koornwinder, and Schempp, Reidel, 1984, 87-128.

2. Recent results for the q-Lagrange inversion formula, Ramanujan Revisited, ed. by Askey, Berndt, Ramanathan, Rankin, Academic Press, 1988, 525-536. pdf

3. An elementary approach to the Macdonald identities, in q-Series and Partitions, ed. by D. Stanton, IMA Volumes in Mathematics and its Applications, Springer, New York, 1989, pp. 139-149. pdf

4. An introduction to group representations and orthogonal polynomials, Orthogonal Polynomials: Theory and Practice, ed. P. Nevai, Proceedings of NATO-ASI, Columbus, 1990, 419-433. pdf

5. More orthogonal polynomials as moments (with M. Ismail), Mathematical Essays in Honor of Gian-Carlo-Rota, Birkhauser 1998, 377-396. pdf

6. The mathematical contributions of Richard Askey (with G. Gasper, M. Ismail, and T. Koornwinder). q-series from a contemporary perspective (South Hadley, MA, 1998), 1-18, Contemp. Math., 254.

7. Three statistics for lattice paths (with D. Kim), Proc. Algebraic Methods and q-Special Functions Workshop CRM, CRM Proc. and Lecture Notes 22 (1999), 201-214. pdf

8. Orthogonal polynomials and combinatorics, in Special Functions 2000: Current Perspective and future directions, Kluwer, 2001, 389-410. pdf

9. Gaussian Integrals and the Rogers-Ramanujan identities, in "Symbolic computation, number theory, special functions, physics, and combinatorics, ed. by F. Garvan and M. Ismail, Kluwer, 2001, 255-266. pdf

10. Enumeration and special functions pdf, in Springer LNM volume 1817, ed. E. Koelink and W. van Assche, 2003, p. 137- 165.

11. Summable sums of hypergeometric series, in Theory and Applications of special Functions, ed. M. Ismail and E. Koelink, p. 401-410, 2005.

12. Moments of orthogonal polynomials and combinatorics (with Sylvie Corteel and Jang Soo Kim), pdf, Recent Trends in Combinatorics, The IMA Volumes in Mathematics and its Applications 159, 2016.

13. Binomial Andrews-Gordon-Bressoud identities, pdf , in Frontiers on Orthogonal Polynomials and q-Series, to appear.

Preprints and other papers

1. Fake Gaussian sequences, pdf

2. Springer's theorem for modular coinvariants of GL_n(F_q) (with V. Reiner and P. Webb) ps

3. Orthogonal polynomials and Smith normal form (with Alex Miller), pdf

4. On the cohomology of Fano varieties and the Springer correspondence (appendix of a paper by T.H. Chen, K. Vilonen, T. Xue) pdf

Books

1. Constructive Combinatorics (with Dennis White), Springer, New York, 1986.

2. q-Series and Partitions (editor), IMA Volumes in Mathematics and its Applications, Vol. 18, Springer, New York, 1989.

3. Invariant Theory and Tableaux (editor), IMA Volumes in Mathematics and its Applications, Vol. 19, Springer, New York, 1989.