(q,t)-deformations of multivariate hook product formulae

2009/09/01 by Soichi Okada, Okada, Soichi
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #math.CO #msc:05E05

paper · pdf · doi:10.48550/arxiv.0909.0086

Improvement of Proposition 4.5 and minor revision

arxiv created 2010/02/16 · arxiv updated 2010/02/26

Abstract

We generalize multivariate hook product formulae for P-partitions. We use Macdonald symmetric functions to prove a (q,t)-deformation of Gansner's hook product formula for the generating functions of reverse (shifted) plane partitions. (The unshifted case has also been proved by Adachi.) For a d-complete poset, we present a conjectural (q,t)-deformation of Peterson--Proctor's hook product formula.

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