Title: On the Algebraic Combinatorics of Injections and its Applications to Injection Codes
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...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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> × S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> , diag(S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> ) × S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-k</sub> ). We use this combinatorial formula to give new Delsarte linear programming bounds on the size of codes over injections.Read More