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arXiv · 2311.03668

On arithmetical structures on K9

Claire Levaillant
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Abstract

We study the arithmetical structures on the complete graph $K_9$. 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 $p$-adic valuations. The proofs are assisted by trees and automata.

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Claire Levaillant. 2023-11-07. On arithmetical structures on K9. https://arxiv.org/abs/2311.03668

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