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The Joint Distribution of Descent and Major Index over Restricted Sets of Permutations
Sylvie Corteel1, Ira M. Gessel2, Carla D. Savage3, and Herbert S. Wilf4
1LRI, CNRS et Universit´e Paris-Sud, Bˆat. 490, F-91405 Orsay, France
corteel@lri.fr
2Department of Mathematics, Brandeis University, Waltham, MA 02454-9110, USA
gessel@brandeis.edu
3Department of Computer Science, College of Engineering, North Carolina State University, Raleigh, NC 27695-8206, USA
savage@csc.ncsu.edu
4Department of Mathematics, School of Arts & Sciences, University of Pennsylvania, Philadelphia, PA 19104-6395, USA
wilf@math.upenn.edu
Annals of Combinatorics 11 (3-4) p.375-386 September, 2007
AMS Subject Classification:05A15, 05A05, 05A30
Abstract:
We compute the joint distribution of descent and major index over permutations of {1,…, n} with no descents in positions {n-i,n-i+1,…,n-1} for fixed i≥0. This was motivated by the problem of enumerating symmetrically constrained compositions and generalizes Carlitz's q-Eulerian polynomial.
Keywords: permutation enumeration, q-Eulerian polynomials, P-partitions

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