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Séminaire Lotharingien de Combinatoire, B51e (2004), 11 pp.

# Toufik Mansour

# Equidistribution and Sign-Balance on 132-Avoiding Permutations

**Abstract.**
Let *R*_{n} be the set of all permutations of length *n* which avoid
132. In this paper we study the statistics *last descent*
("ldes"), *first descent* ("fdes"), *last rise*
("lris"), and *first rise* ("fris") on the set *R*_{n}. In
particular, we prove that the bistatistic ("fris","lris") on the
set of all permutations *R*_{n} \ {*n*...21} and the
bistatistic ("*n*-ldes","*n*-fdes") on the set of all permutations
of *R*_{n} \ {12...*n*} are equidistributed. Furthermore, we
consider the case of sign balance for these statistics on the
set of all permutations *R*_{n}, and we give a combinatorial
interpretation for some of these statistics.

Received: May 26, 2003.
Revised: December 8, 2003, and May 5, 2004.
Accepted: May 22, 2004.

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