On the Algebraic Combinatorics of Injections and its Applications to Injection Codes

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
× S
_n
, diag(S
_k
) × S
_n-k
). We use this combinatorial formula to give new Delsarte linear programming bounds on the size of codes over injections.