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The Joint Distribution of Descent and Major Index over Restricted Sets of Permutations

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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.

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Authors and Affiliations

  1. LRI, CNRS et Université Paris-Sud, Bât. 490, F-91405, Orsay, France

    Sylvie Corteel

  2. Department of Mathematics, Brandeis University, Waltham, MA, 02454-9110, USA

    Ira M. Gessel

  3. Department of Computer Science, College of Engineering, North Carolina State University, Raleigh, NC, 27695-8206, USA

    Carla D. Savage

  4. Department of Mathematics, School of Arts & Sciences, University of Pennsylvania, Philadelphia, PA, 19104-6395, USA

    Herbert S. Wilf

Authors
  1. Sylvie Corteel
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  2. Ira M. Gessel
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  3. Carla D. Savage
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  4. Herbert S. Wilf
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Corresponding author

Correspondence to Sylvie Corteel.

Additional information

Carla D. Savage: Research supported in part by NSF grants DMS-0300034 and INT-0230800.

Received December 19, 2006

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Corteel, S., Gessel, I.M., Savage, C.D. et al. The Joint Distribution of Descent and Major Index over Restricted Sets of Permutations. Ann. Comb. 11, 375–386 (2007). https://doi.org/10.1007/s00026-007-0325-y

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  • DOI: https://doi.org/10.1007/s00026-007-0325-y

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