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(\(q,t\))-deformations of multivariate hook product formulae. (English) Zbl 1228.05048
Summary: 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.

MSC:
05A17 Combinatorial aspects of partitions of integers
05A15 Exact enumeration problems, generating functions
05A05 Permutations, words, matrices
06A07 Combinatorics of partially ordered sets
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