7 papers
New columns in decomposition matrices of symmetric groups for every block
David J. Hemmer, Pavel Turek
The central unsolved problem in the modular representation theory of symmetric groups is to find the decomposition matrices, which describe how irreducible representations in chara…
Divisible Arm Lengths, Crystal Reflections, and Enumeration of Newly Found Decomposition Columns
David J. Hemmer, Pavel Turek
In recent work the authors determine complete columns of symmetric-group decomposition matrices in odd prime characteristic labeled by -regular partitions for which every ho…
Optimal Play, Nontransitivity, and Nash Equilibria in Dice Bingo
David J. Hemmer, Benjamin W. Ong
We study Dice Bingo, a game in which players fill a bingo board whose entries are possible sums of two fair dice. After each roll, a player marks one matching square, an…
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…
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…