Cylindric Partitions
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- by Ira M. Gessel and C. Krattenthaler
- Trans. Amer. Math. Soc. 349 (1997), 429-479
- DOI: https://doi.org/10.1090/S0002-9947-97-01791-1
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Abstract:
A new object is introduced into the theory of partitions that generalizes plane partitions: cylindric partitions. We obtain the generating function for cylindric partitions of a given shape that satisfy certain row bounds as a sum of determinants of $q$-binomial coefficients. In some special cases these determinants can be evaluated. Extending an idea of Burge (J. Combin. Theory Ser. A 63 (1993), 210–222), we count cylindric partitions in two different ways to obtain several known and new summation and transformation formulas for basic hypergeometric series for the affine root system $\widetilde A_{r}$. In particular, we provide new and elementary proofs for two $\widetilde A_{r}$ basic hypergeometric summation formulas of Milne (Discrete Math. 99 (1992), 199–246).References
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Bibliographic Information
- Ira M. Gessel
- Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254–9110
- MR Author ID: 72865
- ORCID: 0000-0003-1061-5095
- Email: ira@cs.brandeis.edu
- C. Krattenthaler
- Affiliation: Institut für Mathematik der Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
- MR Author ID: 106265
- Email: kratt@pap.univie.ac.at
- Received by editor(s): June 1, 1995
- Additional Notes: The first author was supported in part by NSF grant DMS-9306297.
The second author was supported in part by EC’s Human Capital and Mobility Program, grant CHRX-CT93-0400 and the Austrian Science Foundation FWF, grant P10191-MAT - © Copyright 1997 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 349 (1997), 429-479
- MSC (1991): Primary 05A15; Secondary 05A17, 05A30, 05E05, 11P81, 33D20, 33D45
- DOI: https://doi.org/10.1090/S0002-9947-97-01791-1
- MathSciNet review: 1389777