Thumbnail Image
Publication

Improved Bounds for the Index Conjecture in Zero-Sum Theory

Pendleton, Andrew
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).
Description
Date
2024-04-01
Journal Title
Journal ISSN
Volume Title
Publisher
Collections
Undergraduate Honors Theses
Show all metadata
Download Dataset
Files
Pendleton__Andrew_Thesis.pdf
Adobe PDF, 697.94 KB
Rights Holder
Usage License
Embargo
Research Projects
Organizational Units
Journal Issue
Keywords
Citation
Advisor
Ge, Fan
Clare, Pierre
Schueller, Matthew
Department
Mathematics
DOI
URI
https://scholarworks.wm.edu/handle/internal/11593
Embedded videos