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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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