Proof of the Kontsevich Non-Commutative Cluster Positivity Conjecture

Abstract

We extend the Lee-Schiffler Dyck path model to give a proof of the Kontsevich non-commutative cluster positivity conjecture with unequal parameters.

4 pages

References in corpus (3)

• Noncommutative integrability, paths and quasi-determinants
• Non-commutative Laurent phenomenon for two variables
• A short proof of Kontsevich cluster conjecture

Cited by in corpus (9)

• The greedy basis equals the theta basis
• Quantum Cluster Characters
• Greedy bases in rank 2 quantum cluster algebras
• Greedy bases in rank 2 generalized cluster algebras
• The existence of greedy bases in rank 2 quantum cluster algebras
• Positivity for cluster algebras
• Greedy elements in rank 2 cluster algebras
• A combinatorial approach to root multiplicities of rank 2 hyperbolic Kac-Moody algebras
• Noncommutative recursions and the Laurent phenomenon