##### Department of Mathematics,

University of California San Diego

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### Math 296 - Graduate Student Colloquium

## Prof. Brendon Rhoades

#### UC San Diego

## Increasing subsequences, standard bases, and shadow play

##### Abstract:

An {\em increasing subsequence} of a permutation $w \in S_n$ is a sequence of numbers $1 \leq i_1 < \cdots < i_k \leq n$ such that $w(i_1) < \cdots < w(i_k)$. Increasing subsequences have appeared in various guises in combinatorics, probability, and representation theory. We present an algebraic interpretation in terms of a quotient ring inspired by a problem in cryptography. A link between standard monomial bases and Viennot's `shadow line' construction for the Schensted correspondence will play a key role.

Host: Jon Novak

### January 10, 2024

### 3:00 PM

HSS 4025

Research Areas

Combinatorics Representation Theory****************************