Bessenrodt-Stanley polynomials and the octahedron recurrence

TL;DR

This paper demonstrates that Bessenrodt-Stanley polynomials can be represented as solutions to the octahedron recurrence, enabling new explicit formulas and interpretations as path or dimer partition functions.

Contribution

It introduces a novel connection between Bessenrodt-Stanley polynomials and the octahedron recurrence, providing explicit solutions and combinatorial interpretations.

Findings

Polynomials expressed via octahedron recurrence

Explicit formulas as path or dimer partition functions

Generalizations of previous polynomial families

Abstract

We show that a family of multivariate polynomials recently introduced by Bessenrodt and Stanley can be expressed as solution of the octahedron recurrence with suitable initial data. This leads to generalizations and explicit expressions as path or dimer partition functions.