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A step towards the cluster positivity conjecture

By Kyungyong Lee


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.Comment: Comments welcome, v2:16 pages. introduction expanded. section 4 added in order to compare with the known formula when r=2. references added. thank you list added. definitions clarified. This paper is superseded by a joint paper with Ralf Schiffler (

Topics: Mathematics - Quantum Algebra, Mathematics - Algebraic Geometry, Mathematics - Combinatorics
Year: 2011
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