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Chemins sous-diagonaux et tableaux de Young

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Book cover Combinatoire énumérative

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1234))

Abstract

We consider path in the lattice of positive integer coordinate where the possible "moves" are of four kinds : (1) increasing the x coordinate by 1, (2) decreasing the x coordinate by 1, (3) increasing the y coordinate by 1, (4) decreasing the y coordinate by 1. The number of such paths of length ℓ, from (0,0) to any point whose y-coordinate is 0, lying below or touching the main diagonal, is CnCn+1 for ℓ=2n and Cn+1Cn+1 for ℓ=2n+1 where Cn is the Catalan number. We give a bijective proof of this result. As corollary we give exact formulas for the number of standard Young tableaux having n cells and a most k rows in the cases k=4 and k=5.

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Authors and Affiliations

  1. U.E.R. de Mathématiques et d'Informatique, Université de Bordeaux I, 33405, Talence, France

    Dominique Gouyou-Beauchamps

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  1. Dominique Gouyou-Beauchamps
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Gilbert Labelle Pierre Leroux

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© 1986 Springer-Verlag

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Gouyou-Beauchamps, D. (1986). Chemins sous-diagonaux et tableaux de Young. In: Labelle, G., Leroux, P. (eds) Combinatoire énumérative. Lecture Notes in Mathematics, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072513

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  • DOI: https://doi.org/10.1007/BFb0072513

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17207-9

  • Online ISBN: 978-3-540-47402-9

  • eBook Packages: Springer Book Archive

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