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A step towards the cluster positivity conjecture

Published 14 Mar 2011 in math.QA, math.AG, and math.CO | (1103.2726v3)

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

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