A characterization of inverse relations

Discrete Mathematics

Volumn 193, Issue 1-3, 1998, Pages 235-245

  Milne, Stephen C ^a   Bhatnagar, Gaurav ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

'Dual' recurrence relations; (matrix) Bailey transform; Basic hypergeometric series; Derangements; Inverse relations; Pairs of inverse infinite lower triangular matrices; q Chu Vandermonde summation; q Stirling numbers; Shift operators; Stirling numbers

Indexed keywords

EID: 0001061806     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(98)00143-5     Document Type: Article

References (29)

1. G.E. Andrews, Multiple series Rogers-Ramanujan type identities, Pacific J. Math. 114 (1984) 267-283.
2. G.E. Andrews, The fifth and seventh order mock theta functions, Trans. Amer. Math. Soc. 293 (1986) 113-134.
3. G.E. Andrews, q-Series: their development and application in analysis, number theory, combinatorics, physics and computer algebra, NSF CBMS Regional Conf. Series, vol. 66, 1986.
4. G. Bhatnagar, S.C. Milne, Generalized bibasic hypergeometric series and their U(n) extensions, Adv. Math. 131 (1997) 188-252.
5. D.M. Bressoud, A matrix inverse, Proc. Amer. Math. Soc. 88 (1983) 446-448.
6. L. Carlitz, On abelian fields, Trans. Amer. Math. Soc. 35 (1933) 122-136.
7. L. Carlitz, Some inverse relations, Duke Math. J. 40 (1973) 893-901.
8. W.C. Chu, L.C. Hsu, Some new applications of Gould-Hsu inversions, J. Combin. Inform. System Sci. 14 (1990) 1-4.
9. L. Comtet, Advanced Combinatorics, 1970 (J.W. Nienhuys, D. Riedel, English Transl.), Boston 1974.
10. G.P. Egorychev, Integral representations and the computation of combinatorial sums, 'Nauka' Sibirsk. Otdel., Novosibirsk 1977 (English Transl., Transi. Math. Monographs no. 59, Amer. Math. Soc., Providence, RI, 1984).
11. G.P. Egorychev, Integral representations and the computation of combinatorial sums, 'Nauka' Sibirsk. Otdel., Novosibirsk 1977 (English Transl., Transi. Math. Monographs no. 59, Amer. Math. Soc., Providence, RI, 1984).
12. G. Gasper, M. Rahman, Basic Hypergeometric Series, in: G.-C. Rota (Ed.), Encyclopedia of Mathematics and Its Applications, vol. 35, Cambridge Uni. Press, Cambridge, 1990.
13. I. Gessel, D. Stanton, Applications of q-Lagrange inversion to basic hypergeometric series, Trans. Amer. Math. Soc. 277 (1983) 173-201.
14. H.W. Gould, L.C. Hsu, Some new inverse series relations, Duke Math. J. 40 (1973) 885-891.
15. R.L. Graham, D.E. Knuth, O. Patashnik, Concrete Mathematics: a foundation for computer science, Addison-Wesley, Reading, MA, 1989, 2nd ed. 1994.
16. C. Krattenthaler, Operator methods and Lagrange inversion, a unified approach to Lagrange formulas, Trans. Amer. Math. Soc. 305 (1988) 431-465.
17. C. Krattenthaler, A new matrix inverse, Proc. Amer. Math. Soc. 124 (1996) 47-59.
18. S.C. Milne, Restricted growth functions and incidence relations of the lattice of partitions of an n-set, Adv. Math. 26 (1977) 290-305.
19. S.C. Milne, Inversion properties of triangular arrays of numbers Analysis, 1 (1981) 1-7.
20. ℓ Bailey transform and lemma, Bull. Amer. Math. Soc. (N.S.) 26 (1992) 258-263.
21. P.R. de Montmort, Essai d'Analyse sur les Jeux de Hazard, Paris, 1708, 2nd ed. pp. 1713-1714, reprinted as 3rd ed. Chelsea, New York 1980.
22. J. Riordan, Inverse relations and combinatorial identities, Amer. Math. Monthly 71 (1964) 485-498.
23. J. Riordan, Combinatorial Identities, Wiley, New York, 1968.
24. R. Stanley, Enumerative Combinatorics, vol. 1, Wadsworth and Brooks/Cole, Monterey, CA, 1986.
25. J. Stirling, Methodus Differentialis, sive tractatus de summation et interpolation serierum infinitarium, London, 1730 (J. Holliday, English Transl.), The Differential Method: a treatise of the summation and interpolation of infinite series, 1749.
26. J. Stirling, Methodus Differentialis, sive tractatus de summation et interpolation serierum infinitarium, London, 1730 (J. Holliday, English Transl.), The Differential Method: a treatise of the summation and interpolation of infinite series, 1749.
27. P. Théorêt, Relations matricielles pour hyperbinomiales, Ann. Sci. Math. Québec, 19 (1995) 197-212.
28. C. Tweedie, James Stirling: a sketch of his life and works along with his scientific correspondence, Oxford Uni. Press, Oxford, 1922.
29. H, Wilf, D. Zeilberger, Rational function certification of multisum/integral/'q'-identities, Bull. Amer. Math. Soc. (N.S.) 27 (1992) 148-153.