Combinatorial Statistics on Alternating Permutations

Authors:
Serge Dulucq;Rodica Simion
Affiliations:
LaBRI, Université Bordeaux I, 351 cours de la Libération, 30455 Talence, France. E-mail: dulucq@labri.u-bordeaux.fr;Department of Mathematics, The George Washington University, Washington, DC 20052. E-mail: simion@math.gwu.edu
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
1998

Citing 5
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Abstract

We consider two combinatorial statistics on permutations. One isthe genus. The other, \widehat{\rm des}, is defined for alternating permutations, as the sum of the number of descents in thesubwords formed by the peaks and the valleys. We investigatethe distribution of des on genus zero permutations and Baxterpermutations. Our q-enumerative results relate the des statistic to lattice path enumeration, the rank generating function andcharacteristic polynomial of noncrossing partition lattices,and polytopes obtained as face-figures of the associahedron.