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arXiv · 2604.18333

Saturation of Markov Polynomials

Sam J. Evans
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Abstract

Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised version of the Markov equation. The proof we provide is a constructive argument based on the Markov snake graph, a combinatorial object related to Markov numbers, deepening the connection between the Markov equation and combinatorics.

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Sam J. Evans. 2026-04-20. Saturation of Markov Polynomials. https://arxiv.org/abs/2604.18333

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