10 papers
Billiard Orbits in Young Diagrams: Medial Links, Bicycle Spaces, and Domino Tilings
David J. Hemmer
We study diagonal billiard trajectories inside the Young diagram of an integer partition . A trajectory has slope , passes straight through sides shared by adjacent cells…
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…
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…
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…
Generating functions for fixed points of the Mullineux map
David J. Hemmer
Mullineux defined an involution on the set of -regular partitions of . When is prime, these partitions label irreducible symmetric group modules in characteristic .…
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…
Partitions with fixed points in the sequence of first-column hook lengths
Philip Cuthbertson, David J. Hemmer, Brian Hopkins +1
Recently, Blecher and Knopfmacher applied the notion of fixed points to integer partitions. This has already been generalized and refined in various ways such as -fixed points f…