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

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

2011-09-22

arxiv.org/abs/1109.5130v1

Mathematics

Quantum Algebra

13 pages; This paper supersedes the first author's preprint "A step towards the cluster positivity conjecture" (arXiv:1103.272

Scientific paper

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.

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