collaborators

5 papers

math.CO2025

On partitions associated with elementary symmetric polynomials

Cristina Ballantine, Shaheen Nazir, Bridget Eileen Tenner +2

The elementary symmetric partition function is a map on the set of partitions. It sends a partition lambda to the partition whose parts are the summands in the evaluation of the el…

math.CO2025

Equal knapsack identities between symmetric group character degrees

David J. Hemmer, Armin Straub, Karlee J. Westrem

We prove a series of ``knapsack'' type equalities for irreducible character degrees of symmetric groups. That is, we find disjoint subsets of the partitions of so that the two…

math.CO2025

New Identities in the Character Table of Symmetric Groups involving Riordan Numbers

David J. Hemmer, Armin Straub, Karlee Westrem

Amdeberhan recently proposed certain equalities between sums in the character table of symmetric groups. These equalities are between signed column sums in the character table, sum…

math.CO2024

A New Symmetric Function Identity With an Application to symmetric group character values

Karlee J. Westrem

Symmetric functions show up in several areas of mathematics including enumerative combinatorics and representation theory. Tewodros Amdeberhan conjectures equalities of char…

math.CO2024

Palindrome Partitions and the Calkin-Wilf Tree

David J. Hemmer, Karlee J. Westrem

There is a well-known bijection between finite binary sequences and integer partitions. Sequences of length r correspond to partitions of perimeter r+1. Motivated by work on ration…