Geodesic
($q,t$)-deformations of multivariate hook product formulae
Journal of Algebraic Combinatorics, Tome 32 (2010) no. 3, pp. 399-416.

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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.
Keywords: keywords hook product formula, reverse plane partition, Macdonald symmetric functions, $P$-partition, $d$-complete poset 
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     author = {Okada, Soichi},
     title = {($q,t$)-deformations of multivariate hook product formulae},
     journal = {Journal of Algebraic Combinatorics},
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     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2010__32_3_a2/}
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Okada, Soichi. ($q,t$)-deformations of multivariate hook product formulae. Journal of Algebraic Combinatorics, Tome 32 (2010) no. 3, pp. 399-416. http://geodesic.mathdoc.fr/item/JAC_2010__32_3_a2/