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A Bijection from Staircase Tableaux to Inversion Tables, Giving Some Eulerian and Mahonian Statistics

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Abstract

We give a simple bijection between staircase tableaux and inversion tables. Some nice properties of the bijection allow us to easily compute the generating polynomials of subsets of the staircase tableaux. We also give a combinatorial interpretation of some statistics of these tableaux in terms of permutations.

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Authors and Affiliations

  1. LIAFA, CNRS et Université Paris Diderot, 75251, Paris Cedex 13, France

    Sylvie Corteel & Sandrine Dasse-Hartaut

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  1. Sylvie Corteel
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  2. Sandrine Dasse-Hartaut
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Correspondence to Sylvie Corteel.

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Corteel, S., Dasse-Hartaut, S. A Bijection from Staircase Tableaux to Inversion Tables, Giving Some Eulerian and Mahonian Statistics. Ann. Comb. 20, 737–754 (2016). https://doi.org/10.1007/s00026-016-0329-6

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  • DOI: https://doi.org/10.1007/s00026-016-0329-6

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