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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Okada, S. (q,t)-Deformations of multivariate hook product formulae. J Algebr Comb 32, 399–416 (2010). https://doi.org/10.1007/s10801-010-0221-0
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DOI: https://doi.org/10.1007/s10801-010-0221-0