New hook-content formulas for strict partitions

TL;DR

This paper introduces a difference operator for strict partitions and proves a polynomiality property, leading to new hook-content formulas that enhance understanding of strict partition statistics.

Contribution

The paper presents a novel difference operator for strict partitions and derives new hook-content formulas, expanding the mathematical tools for studying strict partition properties.

Findings

Proved polynomiality of certain summations involving hook length and content.

Derived new hook-content formulas for strict partitions.

Introduced a difference operator for functions on strict partitions.

Abstract

We introduce the difference operator for functions defined on strict partitions and prove a polynomiality property for a summation involving the hook length and content statistics. As an application, several new hook-content formulas for strict partitions are derived.