Improved Bounds for the Index Conjecture in Zero-Sum Theory

Author

Andrew Pendleton, William & MaryFollow

Date Thesis Awarded

4-2024

Access Type

Honors Thesis -- Access Restricted On-Campus Only

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Fan Ge

Committee Members

Pierre Clare

Matthew Schueller

Abstract

The Index Conjecture in zero-sum theory states that when n is coprime to 6 and k equals 4, every minimal zero-sum sequence of length k modulo n has index 1. While other values of (k,n) have been studied thoroughly in the last 30 years, it is only recently that the conjecture has been proven for n>10²⁰. In this paper, we prove that said upper bound can be reduced to 4.1*10¹⁴, and lower under certain coprimality conditions. Further, we verify the conjecture for n<1.8*10⁶ through the application of High Performance Computing (HPC).

Recommended Citation

Pendleton, Andrew, "Improved Bounds for the Index Conjecture in Zero-Sum Theory" (2024). Undergraduate Honors Theses. William & Mary. Paper 2115.
https://scholarworks.wm.edu/honorstheses/2115