Mathematics Seminar
Date: Wednesday, 23 October 2024
Time: 2:00 PM
Venue: Seminar Hall
Topology of permutation patterns
Priyavrat Deshpande
Chennai Mathematical Institute.
23-10-24

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Abstract

A permutation of length n is simply an arrangement of numbers from 1 to n and a pattern in it is the existence of a permutation of smaller length. Study of permutation patterns is an active area in enumerative combinatorics. Given a fixed pattern, one can associate a simplicial complex to all the permutations of length n. Recently, researchers have started taking interest in understanding the topology of these simplicial complexes. In this talk, I will illustrate how avoidance or occurrence of certain patterns can be used to express homtopy type of these complexes. Along the way, I will also discuss probabilistic and algorithmic questions in this context. The talk is based on ongoing joint work with Krishna Menon and Anurag Singh.