5 papers
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…
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…
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…
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…
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…