7 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…
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…
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…
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…