The Joint Distribution of Descent and Major Index over Restricted Sets of Permutations |
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| Authors: | Sylvie Corteel Ira M. Gessel Carla D. Savage Herbert S. Wilf |
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| Affiliation: | (1) LRI, CNRS et Université Paris-Sud, Bat. 490, F-91405 Orsay, France;(2) Department of Mathematics, Brandeis University, Waltham, MA 02454-9110, USA;(3) Department of Computer Science, College of Engineering, North Carolina State University, Raleigh, NC 27695-8206, USA;(4) Department of Mathematics, School of Arts & Sciences, University of Pennsylvania, Philadelphia, PA 19104-6395, USA |
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| 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. Received December 19, 2006 |
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| Keywords: | permutation enumeration q-Eulerian polynomials P-partitions |
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