Symmetric and Asymptotically Symmetric Permutations
| dc.creator | Cooper, Joshua | |
| dc.creator | Petrarca, Andrew | |
| dc.date | 2008-01-28 | |
| dc.date.accessioned | 2026-07-07T08:56:46Z | |
| dc.date.available | 2026-07-07T08:56:46Z | |
| dc.description | We consider two related problems arising from a question of R. Graham on quasirandom phenomena in permutation patterns. A ``pattern'' in a permutation $σ$ is the order type of the restriction of $σ: [n] \to [n]$ to a subset $S \subset [n]$. First, is it possible for the pattern counts in a permutation to be exactly equal to their expected values under a uniform distribution? Attempts to address this question lead naturally to an interesting number theoretic problem: when does $k!$ divide $\binom{n}{k}$? Second, if the tensor product of a permutation with large random permutations is random-like in its pattern counts, what must the pattern counts of the original permutation be? A recursive formula is proved which uses a certain permutation ``contraction.'' | |
| dc.description | 13 pages, 3 tables | |
| dc.identifier | https://arxiv.org/abs/0801.4181 | |
| dc.identifier | http://arxiv.org/abs/0801.4181 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146731 | |
| dc.subject | Combinatorics | |
| dc.subject | Number Theory | |
| dc.subject | 05A05; 11B65 | |
| dc.title | Symmetric and Asymptotically Symmetric Permutations | |
| dc.type | text |