Gupta, Ramanujan, Dyson and Ehrhart: Formulas for Partition Functions, Congruences, Cranks, and Polyhedral Geometry

Author

Joselyne Rodriguez, The University of Texas Rio Grande Valley

Date of Award

5-2021

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Dr. Brandt Kronholm

Second Advisor

Dr. Timothy Huber

Third Advisor

Dr. Sergey Grigorian

Abstract

We will revisit Gupta's result regarding properties of a formula for restricted partitions and generalize this. We will then use this result to prove an infinite family of congruences for a certain restricted partition function. We find and prove combinatorial witnesses, also known as cranks, for the congruences using polyhedral geometry.

Comments

Copyright 2021 Joselyne Rodriguez. All Rights Reserved.

https://go.openathens.net/redirector/utrgv.edu?url=https://www.proquest.com/dissertations-theses/gupta-ramanujan-dyson-ehrhart-formulas-partition/docview/2564105920/se-2?accountid=7119

Recommended Citation

Rodriguez, Joselyne, "Gupta, Ramanujan, Dyson and Ehrhart: Formulas for Partition Functions, Congruences, Cranks, and Polyhedral Geometry" (2021). Theses and Dissertations. 951.
https://scholarworks.utrgv.edu/etd/951