Abstract

Matroids give rise to several natural constructions of polytopes. Inspired by this, we examine polytopes that arise from the signed circuits of an oriented matroid. We give the dimensions of these polytopes arising from graphical oriented matroids and their duals. Moreover, we consider polytopes constructed from cocircuits of oriented matroids generated by the positive roots in any type A root system. We give an explicit description of their face structure and determine the Ehrhart series. We also study an action of the symmetric group on these polytopes, giving a full description the subpolytopes fixed by each permutation. These type A polytopes are graphic zonotopes, are polar duals of symmetric edge polytopes, and also make an appearance in Stapledon’s paper introducing Equivariant Ehrhart Theory.

Committee Chair

John Shareshian

Committee Members

Laura Escobar Vega; Martha Precup; Renato Feres; Wanlin Li

Degree

Doctor of Philosophy (PhD)

Author's Department

Mathematics

Author's School

Graduate School of Arts and Sciences

Document Type

Dissertation

Date of Award

5-5-2025

Language

English (en)

Author's ORCID

https://orcid.org/0000-0001-8602-6794

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Mathematics Commons

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