The $*$-Markov equation for Laurent polynomials

TL;DR

This paper introduces a $*$-Markov equation for symmetric Laurent polynomials, exploring its properties and solutions as an analog to the classical Markov equation for integers.

Contribution

It formulates a new equivariant analog of the Markov equation for Laurent polynomials and analyzes its properties and solutions.

Findings

Properties of the classical Markov equation are reflected in the $*$-Markov equation.

Solutions of the $*$-Markov equation exhibit analogous behaviors to integer solutions.

The study provides insights into the structure of symmetric Laurent polynomial equations.

Abstract

We consider the $*$-Markov equation for the symmetric Laurent polynomials in three variables with integer coefficients, which is 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.