4 papers · 1 filter
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…