Plane Partitions and Their Pedestal Polynomials

Abstract

© 2018, Pleiades Publishing, Ltd. For a linear extension P of a partially ordered set S, we consider a generating multivariate polynomial of 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.