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

Toufik Mansour

Equidistribution and Sign-Balance on 132-Avoiding Permutations

Abstract. Let Rn 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 Rn. In particular, we prove that the bistatistic ("fris","lris") on the set of all permutations Rn \ {n...21} and the bistatistic ("n-ldes","n-fdes") on the set of all permutations of Rn \ {12...n} are equidistributed. Furthermore, we consider the case of sign balance for these statistics on the set of all permutations Rn, 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.

The following versions are available: