Speaker: Yuval Roichman (Bar-Ilan University) 

Title: Permutation Statistics on the Alternating Group

Abstract:
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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 index in $S_n$, have received far reaching refinements and
generalizations. Our main goal is to find analogous statistics and
identities for the alternating group $A_n$. 

This is done by choosing appropriate sets of generators for the
corresponding groups. A new statistics for $S_n$, the delent number, is
introduced. This new statistics is involved with new $S_n$ identities,
refining some of the results of Foata-Sch\"utzenberger and Garsia-Gessel.
By a certain covering map from $A_{n+1}$ to $S_n$, such $S_n$ identities
are `lifted' to $A_{n+1}$, yielding the corresponding $A_{n+1}$
identities. 

This is joint work with Amitai Regev.