A Foata bijection for the alternating group and for q analogues

Abstract

The Foata bijection $\Phi :S_n\to S_n$ is extended to the bijections $\Psi :A_{n+1}\to A_{n+1}$ and ${\Psi }_q:S_{n+q-1}\to S_{n+q-1}$, where S_m, A_m are the symmetric and the alternating groups. These bijections imply bijective proofs for recent equidistribution theorems, by Regev and Roichman, for A_{n+1} and for S_{n+q-1}.

16 pages