Abstract
We consider Young tableaux strictly increasing in rows, weakly increasing in columns, and each column having an even number of elements. We show that the number of such tableaux with entries between 1 and n, and having at most 2k rows, is the product
. The proof is mainly bijective, using configurations of non-crossing paths. At the end we need the qd-algorithm from Padé approximants theory.
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Desainte-Catherine, M., Viennot, G. (1986). Enumeration of certain young tableaux with bounded height. In: Labelle, G., Leroux, P. (eds) Combinatoire énumérative. Lecture Notes in Mathematics, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072509
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DOI: https://doi.org/10.1007/BFb0072509
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