Date of Award

2022

Publisher

North Dakota State University

Document Type

Dissertation

Degree Awarded

Doctor of Philosophy (PhD)

Program

Mathematics

Department

Mathematics

College

Science and Mathematics

Faculty Advisor

Striker, Jessica

Description

We define P-strict labelings for a finite poset P as a generalization of semistandard Young tableaux and show that promotion on these objects is in equivariant bijection with a toggle action on B-bounded Q-partitions of an associated poset Q. In many nice cases, this toggle action is conjugate to rowmotion. We apply this result to flagged tableaux, Gelfand-Tsetlin patterns, and symplectic tableaux, obtaining new cyclic sieving and homomesy conjectures. We then study cases in which P is a finite, graded poset other than a chain, yielding new results for products of chains and new perspectives on known conjectures. Additionally, we give resonance results for promotion on P-strict labelings and rowmotion on Q-partitions and demonstrate that P-strict promotion can be equivalently defined using Bender-Knuth and jeu-de-taquin perspectives. Finally, we explore conjectures, related and unrelated to our main theorems, on objects that promise beautiful dynamical properties.

Rights

NDSU policy 190.6.2

Rights Link

https://www.ndsu.edu/fileadmin/policy/190.pdf

Handle Identifier

https://hdl.handle.net/10365/33491

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