On the diagonal hooks of a symmetric partition

TL;DR

This paper provides an explicit formula for the diagonal hook lengths of symmetric partitions using only their symmetric p-core and p-quotient, simplifying the understanding of their structure.

Contribution

It introduces a new explicit formula for diagonal hook lengths based solely on symmetric p-core and p-quotient data, advancing combinatorial partition theory.

Findings

Derived an explicit formula for diagonal hook lengths

Simplified computation using p-core and p-quotient

Enhanced understanding of symmetric partition structure

Abstract

Using only a symmetric p-core partition and p-quotient, we give an explicit formula for the set of diagonal hook lengths of the associated symmetric partition.