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.
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