RS-complete Cycle Types by Prof. Simon Rubinstein-Salzedo, Euler Circle

Title: RS-complete cycle types

Abstract: The Robinson-Schensted Correspondence is a fundamental bijection in algebraic combinatorics, connecting permutations to pairs of standard Young tableaux. This correspondence not only encodes combinatorial data, such as the lengths of increasing and decreasing subsequences in a permutation, but also connects to key theorems in representation theory. In this talk, we will define the Robinson-Schensted Correspondence and explore some of its key properties and applications. Under this correspondence, each permutation gives rise a partition, which corresponds to the shape of the Young tableaux produced. A key question is to determine which cycle types of permutations give rise to all nontrivial RS-shapes. This research is joint work with high-school student Agastya Goel. The talk will be accessible to undergraduates who have studied abstract algebra.