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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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##### References:
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