Geodesic
Equidistribution and Sign-Balance on 132-Avoiding Permutations
Séminaire lotharingien de combinatoire, Tome 51 (2004-2005)

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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. 

@article{SLC_2004-2005_51_a4,
     author = {Toufik Mansour},
     title = {Equidistribution and {Sign-Balance} on {132-Avoiding} {Permutations}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {51},
     year = {2004-2005},
     url = {http://geodesic.mathdoc.fr/item/SLC_2004-2005_51_a4/}
}
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JO  - Séminaire lotharingien de combinatoire
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%T Equidistribution and Sign-Balance on 132-Avoiding Permutations
%J Séminaire lotharingien de combinatoire
%D 2004-2005
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%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2004-2005_51_a4/
%F SLC_2004-2005_51_a4
Toufik Mansour. Equidistribution and Sign-Balance on 132-Avoiding Permutations. Séminaire lotharingien de combinatoire, Tome 51 (2004-2005). http://geodesic.mathdoc.fr/item/SLC_2004-2005_51_a4/