On the Algebraic Combinatorics of Injections and its Applications to Injection Codes
Peter J. Dukes, Ferdinand Ihringer, Nathan Lindzey · IEEE Transactions on Information Theory · 2020
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 (Sk× Sn, diag(Sk) × Sn-k). We use this combinatorial formula to give new Delsarte linear programming bounds on the size of codes over injections.