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Department of Mathematics,
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****************************
