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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.NT2025
Partition-theoretic model of prime distribution
Aidan Botkin, Madeline L. Dawsey, David J. Hemmer +2
We make an application of ideas from partition theory to a problem in multiplicative number theory. We propose a deterministic model of prime number distribution, from first princi…