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On arithmetical structures on K9

Number Theory 2025-04-17 v2 Combinatorics

Abstract

We study the arithmetical structures on the complete graph K9K_9. 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 pp-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

R2 v1 2026-06-28T13:13:31.635Z