Cylindric partitions

被引：59

作者：

Gessel, IM ^{[1
]}

Krattenthaler, C ^{[1
]}

机构：

[1] UNIV VIENNA,INST MATH,A-1090 VIENNA,AUSTRIA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1997年 / 349卷 / 02期

关键词：

cylindric partitions; plane partitions; (A)over-tilde(r) basic hypergeometric series; symmetric functions; Schur functions;

D O I：

10.1090/S0002-9947-97-01791-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 (A) over tilde(r). In particular, we provide new and elementary proofs for two (A) over tilde(r) basic hypergeometric summation formulas of Milne (Discrete Math (1992), 199-246).

引用

页码：429 / 479

页数：51