A step towards the cluster positivity conjecture

Kyungyong Lee

A step towards the cluster positivity conjecture

Quantum Algebra 2011-09-27 v3 Algebraic Geometry Combinatorics

Authors: Kyungyong Lee

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.

Keywords

positive polynomials conjectures and proofs rational maps

Cite

@article{arxiv.1103.2726,
  title  = {A step towards the cluster positivity conjecture},
  author = {Kyungyong Lee},
  journal= {arXiv preprint arXiv:1103.2726},
  year   = {2011}
}

Comments

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 This paper is superseded by a joint paper with Ralf Schiffler (http://arxiv.org/abs/1109.5130)

A step towards the cluster positivity conjecture

Abstract

Keywords

Cite

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