On a Conjecture of Eichhorn, Engle, and Kronholm

Author

• Abigail Magdalena Martinez, The University of Texas Rio Grande Valley

Date of Award

8-1-2026

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Brandt Kronholm

Second Advisor

Runqiao Li

Third Advisor

Josef Sifuentes

Abstract

In this presentation, we will provide evidence that a conjecture on cranks for Gaussian polynomials may be true. We will show a certain infinite family of central coefficients p(2N,4,N) of Gaussian polynomials [N+4 4] in arithmetic progression has Ramanujan-style congruences for all primes ℓ, and that this family of congruences enjoys a common combinatorial witness. Using a combinatorial bijection, we will then show that this combinatorial witness corresponds to the conjecture.

Comments

Copyright 2026 Abigail M. Martinez. All Rights Reserved. https://proquest.com/docview/3408996714

Recommended Citation

Martinez, A. M. (2026). On a Conjecture of Eichhorn, Engle, and Kronholm [Master's thesis, The University of Texas Rio Grande Valley]. ScholarWorks @ UTRGV. https://scholarworks.utrgv.edu/etd/2057