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New identities for binary Krawtchouk polynomials, binomial coefficients and Catalan numbers (1603.09156v2)
Published 30 Mar 2016 in math.CO
Abstract: We obtain new combinatorial identities for integral values of binary Krawtchouk polynomials $K{2m}_p(x)$, $0\le p\le 2m$, by computing the characters of the $p$-exterior representations on certain elements of order 2 of $\mathrm{SO}(2m)$. From this identities, we deduce several new relations for binomial coefficients and Catalan numbers.