4 papers · 1 filter
Partial Lucas-type congruences
Armin Straub
In their study of a binomial sum related to Wolstenholme's theorem, Chamberland and Dilcher prove that the corresponding sequence modulo primes satisfies congruences that are a…
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…
Partitions with Durfee triangles of fixed size
N. Guru Sharan, Armin Straub
A well-studied statistic of an integer partition is the size of its Durfee square. In particular, the number of partitions of with Durfee square of fixed size has…