Solutions of the Yang–Baxter Equation and Automaticity Related to Kronecker Modules by Agustín Moreno Cañadas, Pedro Fernando Fernández Espinosa, Adolfo Ballester-Bolinches

“…Since preprojective Kronecker modules categorize some integer sequences via some appropriated snake graphs, we prove that such modules are automatic and that they induce the automatic sequences of continued fractions.…”
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Snake Graphs Arising from Groves with an Application in Coding Theory by Agustín Moreno Cañadas, Gabriel Bravo Rios, Robinson-Julian Serna

“…It is worth noting that such a number of perfect matchings allows a bijection between the set of snake graphs and the positive <i>continued fractions</i>. Furthermore, perfect matchings of snake graphs have also been used to find closed formulas for cluster variables of some cluster algebras and solutions of the Markov equation, which is a well-known Diophantine equation. …”
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