Plane partitions and their pedestal polynomials

Abstract : Given a partially ordered set S, we define, for a linear extension P of S, a multivariate polynomial, counting certain reverse partitions on S called P-pedestals. We establish a remarkable property of this polynomial: it does not depend on the choice of P. For S a Young diagram, we show that this polynomial generalizes the hook polynomial.
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Oleg Ogievetsky, Senya Shlosman. Plane partitions and their pedestal polynomials. Matematicheskie Zametki / Mathematical Notes, MAIK Nauka/Interperiodica, 2018, 103 (5-6), pp.793-796. ⟨10.1134/S0001434618050115⟩. ⟨hal-01777548⟩

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