# Moscow Mathematical Journal

Volume 22, Issue 1, January–March 2022 pp. 1–68.

The ∗-Markov Equation for Laurent Polynomials

**Authors**:
Giordano Cotti (1) and Alexander Varchenko (2)

**Author institution:**(1) Faculdade de Ciências da Universidade de Lisboa - Grupo de Física Matemática, Campo Grande Edifício C6, 1749-016 Lisboa, Portugal

(2) Department of Mathematics, University
of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3250, USA;

Faculty of Mathematics and Mechanics, Lomonosov Moscow State
University, Leninskiye Gory 1, 119991 Moscow GSP-1, Russia

**Summary: **

We consider the $*$-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which appears as an equivariant analog of the classical Markov equation for integers. We study how the properties of the Markov equation and its solutions are reflected in the properties of the $*$-Markov equation and its solutions.

2020 Math. Subj. Class. 11D25, 14F08, 34M40

**Keywords:**Markov equation, symmetric Laurent polynomial, trees, Poisson structure.

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