Another refinement of the Bender-Knuth (ex-)Conjecture
Combinatorics
2007-05-23 v1
Abstract
We compute the generating function of column-strict plane partitions with parts in {1,2,...,n}, at most c columns, p rows of odd length and k parts equal to n. This refines both, Krattenthaler's ["The major counting of nonintersecting lattice paths and generating functions for tableaux", Mem. Amer. Math. Soc. 115 (1995)] and the author's ["A method for proving polynomial enumeration formulas", preprint] refinement of the Bender-Knuth (ex-)Conjecture. The result is proved by an extension of the method for proving polynomial enumeration formulas which was introduced by the author to q-quasi-polynomials.
Cite
@article{arxiv.math/0401235,
title = {Another refinement of the Bender-Knuth (ex-)Conjecture},
author = {Ilse Fischer},
journal= {arXiv preprint arXiv:math/0401235},
year = {2007}
}