Date of Award

Spring 6-8-2024

Document Type

Thesis (Ph.D.)

Department or Program

Mathematics

First Advisor

Sergi Elizalde

Abstract

Over the past decade since the term `dynamical algebraic combinatorics' was coined there has been a tremendous amount of activity in the field. Adding to that growing body of work this thesis hopes to be a step towards a broader study of pattern avoidance within dynamical algebraic combinatorics and helps initiate that by considering an action of rowmotion on 321-avoiding permutations. Additionally within we show the first known instance of piecewise-linear rowmotion periodicity for an infinite family of posets that does not follow from a more general birational result. Finally we show that the code of permutation restricted to permutations that avoid 2143 induces a map to permutations that avoid 132 that is both order and height preserving when pattern avoidance classes are considered as subposets of the Bruhat order for any length permutation.

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