Saturation of Markov Polynomials

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.