A step towards the cluster positivity conjecture

2011/03/14 by Kyungyong Lee, Lee, Kyungyong
Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.AG #math.CO #math.QA

paper · pdf · doi:10.48550/arxiv.1103.2726

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 This paper is superseded by a joint paper with Ralf Schiffler (http://arxiv.org/abs/1109.5130)

arxiv created 2011/09/26 · arxiv updated 2011/09/27

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.

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