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Enumeration formulas for young tableaux in a diagonal strip

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Abstract

We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. André on the number of up-down permutations. The analysis uses a transfer operator approach extending the method of Elkies, combined with an identity expressing the volume of a certain polytope in terms of a Schur function.

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Authors and Affiliations

  1. Mathematical and Algorithmic Sciences, Bell Laboratories, Murray Hill, NJ, USA

    Yuliy Baryshnikov

  2. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Dan Romik

Authors
  1. Yuliy Baryshnikov
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  2. Dan Romik
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Correspondence to Yuliy Baryshnikov.

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Baryshnikov, Y., Romik, D. Enumeration formulas for young tableaux in a diagonal strip. Isr. J. Math. 178, 157–186 (2010). https://doi.org/10.1007/s11856-010-0061-6

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  • DOI: https://doi.org/10.1007/s11856-010-0061-6

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