UW Combinatorics and Geometry Seminar: Brendon Rhoades

The Schensted correspondence is a bijection between permutations in Sn and pairs of standard Young tableaux (P,Q) with n boxes which have the same shape. This bijection has remarkable properties in algebraic and enumerative combinatorics. Motivated by a problem in cryptography, we study a graded quotient Rn of the polynomial ring in n×n variables whose standard monomial theory encodes Viennot's shadow line formulation of the Schensted correspondence. The quotient ring Rn may be understood as coming from the locus of permutation matrices via the machine of orbit harmonics. I will report on work of my student Moxuan Liu who has extended this theory to colored permutation groups.