The Affinity of a Permutation of a Finite Vector Space
| dc.creator | Clark, W. Edwin | |
| dc.creator | Hou, Xiang-dong | |
| dc.creator | Mihailovs, Alec | |
| dc.date | 2004-07-08 | |
| dc.date.accessioned | 2026-07-07T05:10:07Z | |
| dc.date.available | 2026-07-07T05:10:07Z | |
| dc.description | For a permutation f of an n-dimensional vector space V over a finite field of order q we let k-affinity(f) denote the number of k-flats X of V such that f(X) is also a k-flat. By k-spectrum(n,q) we mean the set of integers k-affinity(f) where f runs through all permutations of V. The problem of the complete determination of k-spectrum(n,q) seems very difficult except for small or special values of the parameters. However, we are able to establish that k-spectrum(n,q) contains 0 in the following cases: (i) q>2 and 0<k<n; (ii) q=2, 2<k<n; (iii) q=2, k=2, odd n>2. The maximum of k-affinity(f) is, of course, obtained when f is any semi-affine mapping. We conjecture that the next to largest value of k-affinity(f) is when f is a transposition and we are able to prove this when q=2, k=2, n>2 and when q>2, k=1, n>1. | |
| dc.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/math/0407148 | |
| dc.identifier | http://arxiv.org/abs/math/0407148 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71829 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A20, 05D40, 05E20, 52C45 | |
| dc.title | The Affinity of a Permutation of a Finite Vector Space | |
| dc.type | text |