A Foata bijection for the alternating group and for -analogues.
Dan Bernstein, Amitai Regev · Séminaire Lotharingien de Combinatoire [electronic only] · 2005
The Foata bijection : Sn ! Sn is extended to the bijections : An+1 ! An+1 and q : 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.