Year: 2026
Type: preprint
Abstract: Laurent phenomenon algebras were introduced by Lam and Pylyavskyy as a generalisation of cluster algebras. For a family associated with directed graphs, they showed that every cluster variable is a Laurent polynomial in the variables of any cluster and conjectured that these expansions have nonnegative coefficients. We prove this conjecture for all directed graphs without loops or multiple edges with respect to an arbitrary seed cluster.
Source: arXiv (Cornell University)
Author: Glew, Ross
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
Award: G8284209191
OpenAlex ID: W7220897644