Séminaire Lotharingien de Combinatoire, 84B.94 (2020), 12 pp.

Peter Dukes, Ferdinand Ihringer and Nathan Lindzey

On the Algebraic Combinatorics of Injections

Abstract. We consider the algebraic combinatorics of the set of injections from a k-element set to an n-element set. In particular, we give a new combinatorial formula for the spherical functions of the Gelfand pair (S_k x S_n, diag(S_k) x S_n-k). We use this combinatorial formula to give new LP bounds on the size of codes over injections.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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