Permutation Statistics on the Alternating Group
| dc.creator | Regev, Amitai | |
| dc.creator | Roichman, Yuval | |
| dc.date | 2003-02-25 | |
| dc.date.accessioned | 2026-07-07T04:55:33Z | |
| dc.date.available | 2026-07-07T04:55:33Z | |
| dc.description | Let $A_n\subseteq S_n$ denote the alternating and the symmetric groups on $1,...,n$. MacMahaon's theorem, about the equi-distribution of the length and the major indices in $S_n$, has received far reaching refinements and generalizations, by Foata, Carlitz, Foata-Schutzenberger, Garsia-Gessel and followers. Our main goal is to find analogous statistics and identities for the alternating group $A_{n}$. A new statistic for $S_n$, {\it the delent number}, is introduced. This new statistic is involved with new $S_n$ equi-distribution identities, refining some of the results of Foata-Schutzenberger and Garsia-Gessel. By a certain covering map $f:A_{n+1}\to S_n$, such $S_n$ identities are `lifted' to $A_{n+1}$, yielding the corresponding $A_{n+1}$ equi-distribution identities. | |
| dc.description | 45 pages | |
| dc.identifier | https://arxiv.org/abs/math/0302301 | |
| dc.identifier | http://arxiv.org/abs/math/0302301 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66617 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A15, 05A19 | |
| dc.title | Permutation Statistics on the Alternating Group | |
| dc.type | text |