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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