On arithmetical structures on K9
Number Theory
2025-04-17 v2 Combinatorics
Abstract
We study the arithmetical structures on the complete graph . Our method is based on studying the solutions to writing the unit as a sum of 9 unit fractions. We work from the perspective of the Diophantine equation and use some elementary properties on the -adic valuations. The proofs are assisted by trees and automata.
Cite
@article{arxiv.2311.03668,
title = {On arithmetical structures on K9},
author = {Claire Levaillant},
journal= {arXiv preprint arXiv:2311.03668},
year = {2025}
}
Comments
74 pages