Rook theory and hypergeometric series

Advances in Applied Mathematics

Volumn 17, Issue 4, 1996, Pages 408-459

  Haglund, James ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030524994     PISSN: 01968858     EISSN: None     Source Type: Journal    
DOI: 10.1006/aama.1996.0017     Document Type: Article

References (45)

1. [Bai] W. N. Bailey, "Generalized Hypergeometric Series," Vol. 32, Cambridge Univ. Press, Cambridge, 1935.
2. [Bow1] D. Bowman, "q-Series, Partitions, and Continued Fractions," Ph.D. thesis. University of California, Los Angeles, 1993.
3. [Bow2] D. Bowman, A general Heine transformation and symmetric polynomials of Rogers, preprint, 1995.
4. [Cho1] T. Y. Chow, The path-cycle symmetric function of a digraph, Adv. Math., 118 (1996), 71-98.
5. [Cho2] T. Y. Chow, "Symmetric Function Generalizations of Graph Polynomials," Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1995.
6. [Cho3] T. Y. Chow, A short proof of the rook reciprocity theorem, Electron. J. Combin. 3 (1996).
7. [Chu] W. Chu, Partial fractions and bilateral summations, J. Math. Phys. 35 (1994), 2036-2042.
8. [ChRo] Y.-C. Chen and G.-C. Rota, q-Analogs of the principle of inclusion-exclusion and permutations with restricted position, Discuss. Math. 104 (1992), 7-22.
9. [ChG] F. Chung and R. Graham, On digraph polynomials, preprint, 1993.
10. [Din1] K. Ding, Invisible permutations and rook placements on a Ferrers board, preprint, 1992.
11. [Din2] K. Ding, "Rook Placements and Cellular Decomposition of Partition Varieties," Ph.D. thesis, University of Wisconsin-Madison, 1993.
12. [DiR] J. F. Dillon and D. P. Roselle, Simon Newcomb's problem, SIAM J. Appl. Math. 17 (1969), 1086-1093.
13. [Dwo] M. Dworkin, Factorization of the Cover Polynomial, preprint, 1995.
14. [EHR] R. Ehrenborg, J. Haglund, and M. Readdy, Colored juggling patterns and weighted rook placements, manuscript in preparation.
15. [Erd] A. Erdélyi, Integraldarstellungen hypergeometrischer funktionen, Quart. J. Math. 8 (1937), 267-277.
16. [Fine] N. Fine, "Basic Hypergeometric Series and Applications," Amer. Math. Soc., Providence, RI, 1991.
17. [FoSu] D. C. Foata and M. P. Schützenberger, On the rook polynomials of Ferrers relations, in "Combinatorial Theory and Its Applications, 2," Colloq. Math. Janos Bolyai, Vol. 4, pp. 413-436, North-Holland, Amsterdam, 1970.
18. [GaRe] A. J. Garsia and J. B. Remmel, q-Counting rook configurations, J. Combin. Theory Ser. A 41 (1986), 246-275.
19. [GaRa] G. Gasper and M. Rahman, Basic hypergeometric series, in "Encyclopedia of Math. and Its Applications," Cambridge Univ. Press, Cambridge, MA, 1990.
20. [Gasp] G. Gasper, Summation formulas for basic hypergeometric series, Siam. J. Math. Anal. 12 (1981), 196-200.
21. [Gau] C. F. Gauss, Disquisitiones generales circa seriem infinitam . . . , Comm. Soc. Reg. Sci. Gött. Rec.; reprinted in "Werke 3," Vol. II, pp. 123-162, Gedruckt in der Dieterichschen Universitatdruckerei (W. F. Kaestner): Göttingen 1876.
22. [Ges1] I. M. Gessel, Generalized rook polynomials and orthogonal polynomials, in "q-Series and Partitions" (Dennis Stanton, Ed.), IMA Volumes in Mathematics and Its Applications, pp. 159-176, Springer-Verlag, New York, 1989.
23. [Ges2] I. M. Gessel, private communication.
24. [GJW1] J. R. Goldman, J. T. Joichi, and D. E. White, Rook theory. I. Rook equivalence of Ferrers boards, Proc. Amer. Math. Soc. 52 (1975), 485-492.
25. [GJW2] J. R. Goldman, J. T. Joichi, and D. E. White, Rook theory. IV. Orthogonal sequences of rook polynomials, Stud. Appl. Math. 56 (1977), 267-272.
26. [Hag1] J. Haglund, "Compositions, Rook Placements, and Permutations of Vectors," Ph.D. thesis, University of Georgia, Athens, GA, 1993.
27. [Hag2] J. Haglund, Compositions and rook placements, preprint, 1994.
28. [JoRo] S. A. Joni and G.-C. Rota, A vector space analog of permutations with restricted position, J. Combin. Theory Ser. A 29 (1980), 59-73.
29. [KaRi] I. Kaplansky and J. Riordan, The problem of the rooks and its applications, Duke Math. J. 13 (1946), 259-268.
30. [Kar] P. W. Karlsson, Hypergeometric functions with integral parameter differences, J. Math. Phys. 12 (1971), 270-271.
31. [Mac] I. G. Macdonald, "Symmetric Functions and Hall Polynomials," Oxford Univ. Press, Oxford, 1979.
32. [MacR] T. MacRobert, "Functions of a Complex Variable," 5th ed. MacMillan & Co., London, 1962.
33. [Min] B. M. Minton, Generalized hypergeometric functions of unit argument, J. Math. Phys. 11 (1970), 1375-1376.
34. n(ζ,p,v), Bull. Amer. Math. Soc. 51 (1945), 714-723.
35. [Rai2] E. D. Rainville, "Special Functions," MacMillan Co., New York, 1960.
36. [Rio] J. Riordan, "An Introduction to Combinatorial Analysis," Wiley, New York, 1958.
37. [Sch] M. Schlosser, private communication.
38. [Sea1] D. B. Sears, On the transformation theory of hypergeometric functions and cognate trigonometric series, Proc. London Math. Soc. (2) 53 (1951), 138-157.
39. [Sea2] D. B. Sears, Transformations of basic hypergeometric functions of any order, Proc. London Math. Soc. (2) 53 (1951), 181-191.
40. [Shev] V. S. Shevelev, Some problems of the theory of enumerating the permutations with restricted positions, J. Soviet Math. 61 (1992), 2272-2317.
41. [Sla] L. J. Slater, "Generalized Hypergeometric Functions," Cambridge Univ. Press, Cambridge, 1966.
42. [Sol] L. Solomon, The Bruhat decomposition, Tits system, and Iwahori ring for the monoid of matrices over a finite field, Geom. Dedicata 36 (1990), 15-49.
43. [StS] R. Stanley and J. Stembridge, On immanants of Jacobi-Trudi matrices and permutations with restricted position, J. Combin. Theory Ser. A 62 (1993), 261-279.
44. [Ste] E. Steingrimsson, A chromatic partition polynomial, in "Proceedings of the Seventh International Conference on Formal Power Series and Algebraic Combinatorics, Marne-La-Vallée, France, 1995," pp. 511-521.
45. [WaW] M. Wachs and D. White, p, q-Stirling numbers and set partition statistics, J. Combin. Theory Ser. A 56 (1991), 27-46.