A step towards the cluster positivity conjecture

TL;DR

This paper proves Kontsevich's conjecture that iterations of a specific noncommutative rational map produce Laurent polynomials with nonnegative integer coefficients, advancing understanding in noncommutative algebra.

Contribution

It provides a proof for Kontsevich's conjecture on the positivity of Laurent polynomial coefficients generated by a noncommutative rational map.

Findings

Iterations yield noncommutative Laurent polynomials with nonnegative coefficients

Supports the cluster positivity conjecture in noncommutative settings

Advances theoretical understanding of noncommutative rational maps

Abstract

We prove a conjecture of Kontsevich, which asserts that the iterations of the noncommutative rational map $F_r:(x,y)-->(xyx^{-1},(1+y^r)x^{-1})$ are given by noncommutative Laurent polynomials with nonnegative integer coefficients.