an:05859685
Zbl 1276.16025
Di Francesco, Philippe; Kedem, Rinat
Discrete non-commutative integrability: proof of a conjecture by M. Kontsevich
EN
Int. Math. Res. Not. 2010, No. 21, 4042-4063 (2010).
00271259
2010
j
16S38 37F10 13F60 05C90
Summary: We prove a conjecture of Kontsevich regarding the solutions of rank 2 recursion relations for non-commutative variables, which, in the commutative case, reduce to rank 2 cluster algebras of affine type. The conjecture states that solutions are positive Laurent polynomials in the initial cluster variables. We prove this by the use of a non-commutative version of the path models, which we used for the commutative case.