Zeilberger's KOH theorem and the strict unimodality of q-binomial coefficients

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Conference Proceeding

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A recent nice result due to I. Pak and G. Panova is the strict unimodality of the -binomial coefficients . Since their proof used representation theory and Kronecker coefficients, the authors also asked for an argument that would employ Zeilberger's KOH theorem. In this note, we give such a proof. Then, as a further application of our method, we also provide a short proof of their conjecture that the difference between consecutive coefficients of can get arbitrarily large, when we assume that is fixed and is large enough.

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© Copyright 2015 American Mathematical Society. Publisher’s version of record: https://doi.org/10.1090/S0002-9939-2015-12510-5

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Proceedings of the American Mathematical Society