Séminaire Lotharingien de Combinatoire, B53b (2005), 16 pp.

Dan Bernstein and Amitai Regev

A Foata Bijection for the Alternating Group and for q-Analogues

Abstract. The Foata bijection \Phi:Sn->Sn is extended to the bijections \Psi:An+1->An+1 and \Psiq:Sn+q-1->Sn+q-1, where Sm, Am are the symmetric and the alternating groups. These bijections imply bijective proofs for recent equidistribution theorems, by Regev and Roichman, for An+1 and for Sn+q-1.

Received: March 20, 2005. Accepted: April 23, 2005. Final Version: April 25, 2005.

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