Colloquium: RS-complete cycle types

Abstract: The Robinson-Schensted Correspondence, a fundamental bijection in algebraic combinatorics, establishes a connection between permutations and pairs of standard Young tableaux. This correspondence not only encodes combinatorial information, such as the lengths of increasing and decreasing subsequences within a permutation, but also links to significant theorems in representation theory. In this talk, we will define the Robinson-Schensted Correspondence and delve into its key properties and applications. Under this correspondence, each permutation generates a partition, which corresponds to the shape of the Young tableaux produced. A crucial question arises: which cycle types of permutations yield all nontrivial RS-shapes? This research is a collaborative effort with high school student Agastya Goel.

Host: Silas Johnson

Reception: There will be light refreshments served in Cupples I Hall, Room 200 (Lounge) following the talk.