Date of Award

2018

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

Motivated by the study of polytopes formed as the convex hull of permutation matrices and alternating sign matrices, several new families of polytopes are defined as convex hulls of sign matrices, which are certain {0,1,-1}--matrices in bijection with semistandard Young tableaux. This bijection is refined to include standard Young tableau of certain shapes. One such shape is counted by the Catalan numbers, and the convex hull of these standard Young tableaux form a Catalan polytope. This Catalan polytope is shown to be integrally equivalent to the order polytope of the triangular poset: therefore the Ehrhart polynomial and volume can be combinatorial interpreted. Various properties of all of these polytope families are investigated, including their inequality descriptions, vertices, facets, and face lattices, as well as connections to alternating sign matrix polytopes, and transportation polytopes.

Rights

NDSU Policy 190.6.2

Rights Link

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

Author ORCID Identifier

0000-0001-5286-4052

Handle Identifier

https://hdl.handle.net/10365/28767

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