A method for proving polynomial enumeration formulas

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:111

Article

Fischer, I

关键词: polynomial enumeration formulas;    generating functions;    plane partitions;    tableaux;   

DOI  :  10.1016/j.jcta.2004.11.007

来源: Elsevier

【 摘 要 】

We present an elementary method for proving enumeration formulas which are polynomials in certain parameters if others are fixed and factorize into distinct linear factors over Z. Roughly speaking the idea is to prove such formulas by explaining their zeros using an appropriate combinatorial extension of the objects under consideration to negative integer parameters. We apply this method to prove a new refinement of the Bender-Knuth (ex-)Conjecture, which easily implies the Bender-Knuth (ex-)Conjecture itself. This is probably the most elementary way to prove this result currently known. Furthermore we adapt our method to q-polynomials, which allows us to derive generating function results as well. Finally we use this method to give another proof for the enumeration of semistandard tableaux of a fixed shape which differs from our proof of the Bender-Knuth (ex-)Conjecture in that it is a multivariate application of our method. (c) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free