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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*:*S*_{n}->*S*_{n}
is extended to the
bijections
*\Psi*:*A*_{n+1}->*A*_{n+1}
and *\Psi*_{q}:*S*_{n+q-1}->*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}.

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

The following versions are available: