Another refinement of the Bender-Knuth (ex-)Conjecture

Details Another refinement of the Bender-Knuth (ex-)Conjecture Another refinement of the Bender-Knuth (ex-)Conjecture

2004-01-19

arxiv.org/abs/math/0401235v1

Mathematics

Combinatorics

Scientific paper

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.

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