Symmetric Functions and Caps
| dc.creator | Carlsson, Erik | |
| dc.date | 2008-08-21 | |
| dc.date.accessioned | 2026-07-07T09:57:39Z | |
| dc.date.available | 2026-07-07T09:57:39Z | |
| dc.description | Given a finite subset S in F_p^d, let a(S) be the number of distinct r-tuples (x_1,...,x_r) in S such that x_1+...+x_r = 0. We consider the "moments" F(m,n) = sum_|S|=n a(S)^m. Specifically, we present an explicit formula for F(m,n) as a product of two matrices, ultimately yielding a polynomial in q=p^d. The first matrix is independent of n while the second makes no mention of finite fields. However, the complexity of calculating each grows with m. The main tools here are the Schur-Weyl duality theorem, and some elementary properties of symmetric functions. This problem is closely to the study of maximal caps. | |
| dc.description | 11 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/0808.2849 | |
| dc.identifier | http://arxiv.org/abs/0808.2849 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167420 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20K01 | |
| dc.title | Symmetric Functions and Caps | |
| dc.type | text |