Plane partitions and their pedestal polynomials

TL;DR

This paper introduces a new multi-variable polynomial generalization of the hook polynomial for any partially ordered set, expanding the combinatorial tools available for studying plane partitions.

Contribution

It defines a novel polynomial called the pedestal polynomial that generalizes the hook polynomial to arbitrary posets.

Findings

Introduces the pedestal polynomial for arbitrary posets

Generalizes the hook polynomial to a multi-variable setting

Provides new combinatorial interpretations and properties

Abstract

We define, for an arbitrary partially ordered set, a multi-variable polynomial generalizing the hook polynomial.