q Statistics on $S_n$ and Pattern Avoidance
| dc.creator | Regev, Amitai | |
| dc.creator | Roichman, Yuval | |
| dc.date | 2003-05-28 | |
| dc.date.accessioned | 2026-07-07T04:58:20Z | |
| dc.date.available | 2026-07-07T04:58:20Z | |
| dc.description | Natural q analogues of classical statistics on the symmetric groups $S_n$ are introduced; parameters like: the q-length, the q-inversion number, the q-descent number and the q-major index. MacMahon's theorem about the equi-distribution of the inversion number and the reverse major index is generalized to all positive integers q. It is also shown that the q-inversion number and the q-reverse major index are equi-distributed over subsets of permutations avoiding certain patterns. Natural q analogues of the Bell and the Stirling numbers are related to these q statistics -- through the counting of the above pattern-avoiding permutations. | |
| dc.description | 40 pages | |
| dc.identifier | https://arxiv.org/abs/math/0305393 | |
| dc.identifier | http://arxiv.org/abs/math/0305393 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67595 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 05A19 | |
| dc.title | q Statistics on $S_n$ and Pattern Avoidance | |
| dc.type | text |