Equal knapsack identities between symmetric group character degrees
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914069486764032 |
|---|---|
| author | Hemmer, David J. Straub, Armin Westrem, Karlee J. |
| author_facet | Hemmer, David J. Straub, Armin Westrem, Karlee J. |
| contents | 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 $n$ so that the two corresponding character-degree sums are equal. Our main result refines our recent description of the Riordan numbers as the sum of all character degrees $f^λ$ where $λ$ is a partition of $n$ into three parts of the same parity. In particular, the sum of the ``fat-hook'' degrees $f^{(k,k,1^{n-2k})}+f^{(k+1,k+1,1^{n-2k-2})}$ equals the sum of all $f^λ$ where $λ$ has three parts, with the second equal to $k$ and the second and third of equal parity. We further prove an infinite family of additional ``knapsack'' identities between character degrees |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_00301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equal knapsack identities between symmetric group character degrees Hemmer, David J. Straub, Armin Westrem, Karlee J. Combinatorics 05E10 (Primary), 20C15 (Secondary) 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 $n$ so that the two corresponding character-degree sums are equal. Our main result refines our recent description of the Riordan numbers as the sum of all character degrees $f^λ$ where $λ$ is a partition of $n$ into three parts of the same parity. In particular, the sum of the ``fat-hook'' degrees $f^{(k,k,1^{n-2k})}+f^{(k+1,k+1,1^{n-2k-2})}$ equals the sum of all $f^λ$ where $λ$ has three parts, with the second equal to $k$ and the second and third of equal parity. We further prove an infinite family of additional ``knapsack'' identities between character degrees |
| title | Equal knapsack identities between symmetric group character degrees |
| topic | Combinatorics 05E10 (Primary), 20C15 (Secondary) |
| url | https://arxiv.org/abs/2510.00301 |