Document Type
Article
Publication Date
3-27-2026
Department
Department of Mathematical Sciences
Abstract
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, summing over the rows labeled by partitions in Ev(λ), where λ is a partition of n with r nonzero parts and Ev(λ) is a multiset containing 2r partitions of 2n. While we observe that these equalities are not true in general, we prove that they do hold in interesting special cases. These lead to new equalities between sums of degrees of irreducible characters for the symmetric group and a new combinatorial interpretation for the Riordan numbers in terms of degrees of irreducible characters labeled by partitions with three parts of the same parity. This is the first, to our knowledge, theorem about degrees of symmetric group characters with parity conditions imposed on the partitions indexing the characters.
Publication Title
The Electronic Journal of Combinatorics
Recommended Citation
Hemmer, D.,
Straub, A.,
&
Westrem, K. J.
(2026).
New Identities in the Character Table of Symmetric Groups involving Riordan Numbers.
The Electronic Journal of Combinatorics,
33(1).
http://doi.org/https://doi.org/10.37236/14401
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p2/2599
Creative Commons License
This work is licensed under a Creative Commons Attribution-No Derivative Works 4.0 International License.
Version
Publisher's PDF
Publisher's Statement
© The authors. 2026. Publisher’s version of record: https://doi.org/10.37236/14401