This material has been published in Trans. Amer. Math. Soc. 349 (1997), 429-479, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the American Mathematical Society. This material may not be copied or reposted without explicit permission.

Ira M. Gessel and Christian Krattenthaler

Cylindric partitions

(58 pages)

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), by counting cylindric partitions in two different ways we obtain several known and new summation and transformation formulas for basic hypergeometric series for the affine root system Ãr. In particular, we provide new and elementary proofs for two Ãr basic hypergeometric summation formulas of Milne (Discrete Math. 99 (1992), 199-246).

The following versions are available:

Back to Christian Krattenthaler's home page.