A shadow Markov equation
Nathan Bonin, Valentin Ovsienko
TL;DR
This paper introduces a superanalogue of the classical Markov equation that characterizes shadow Markov numbers and is invariant under cluster algebra mutations, expanding the mathematical understanding of these structures.
Contribution
The paper presents a novel superanalogue of the Markov equation and links it to cluster algebra invariance, providing new insights into shadow Markov numbers.
Findings
Defined a superanalogue of the Markov equation
Established invariance under cluster algebra mutations
Connected shadow Markov numbers to the new equation
Abstract
We introduce a superanalogue of the classical Markov equation. This equation characterizes the ``shadow Markov numbers'' recently considered by one of us. We show that this equation is characterized by invariance by cluster algebra mutations.
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Taxonomy
TopicsAdvanced Database Systems and Queries · Complex Network Analysis Techniques · Stochastic processes and statistical mechanics