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Proof of a positivity conjecture of M. Kontsevich on non-commutative cluster variables

Published 22 Sep 2011 in math.QA, math.AG, and math.CO | (1109.5130v1)

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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