Snake Graphs for Graph LP Algebras
Combinatorics
2023-12-20 v1
Abstract
Graph LP algebras are a generalization of cluster algebras introduced by Lam and Pylyavskyy. We provide a combinatorial proof of positivity for certain cluster variables in these algebras. This proof uses a hypergraph generalization of snake graphs, a class of planar graphs which were used by Musiker, Schiffler, and Williams to prove positivity for cluster algebras from surfaces. These results extend those given in our previous paper, where we used a related combinatorial object known as a -path.
Cite
@article{arxiv.2312.12313,
title = {Snake Graphs for Graph LP Algebras},
author = {Esther Banaian and Sunita Chepuri and Elizabeth Kelley and Sylvester W. Zhang},
journal= {arXiv preprint arXiv:2312.12313},
year = {2023}
}