Geodesic
A Foata Bijection for the Alternating Group and for q-Analogues
Séminaire lotharingien de combinatoire, Tome 53 (2005-2006)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@article{SLC_2005-2006_53_a1,
     author = {Dan Bernstein and Amitai Regev},
     title = {A {Foata} {Bijection} for the {Alternating} {Group} and for {q-Analogues}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {53},
     year = {2005-2006},
     url = {http://geodesic.mathdoc.fr/item/SLC_2005-2006_53_a1/}
}
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Dan Bernstein; Amitai Regev. A Foata Bijection for the Alternating Group and for q-Analogues. Séminaire lotharingien de combinatoire, Tome 53 (2005-2006). http://geodesic.mathdoc.fr/item/SLC_2005-2006_53_a1/