New identities for binary Krawtchouk polynomials, binomial coefficients and Catalan numbers

Abstract

We obtain new combinatorial identities for integral values of binary Krawtchouk polynomials $K_p^{2m}(x)$, $0\le p\le 2m$, 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.

25 pages, 1 table, 28 references. Fixed some typos, new formulas added

References in corpus (2)

• (Z_2^k)-manifolds are isospectral on forms
• A variant of Touchard's Catalan number identity