Rooted Clusters for Graph LP Algebras
Combinatorics
2022-11-28 v3
Abstract
LP algebras, introduced by Lam and Pylyavskyy, are a generalization of cluster algebras. These algebras are known to have the Laurent phenomenon, but positivity remains conjectural. Graph LP algebras are finite LP algebras encoded by a graph. For the graph LP algebra defined by a tree, we define a family of clusters called rooted clusters. We prove positivity for these clusters by giving explicit formulas for each cluster variable. We also give a combinatorial interpretation for these expansions using a generalization of -paths.
Keywords
Cite
@article{arxiv.2107.14785,
title = {Rooted Clusters for Graph LP Algebras},
author = {Esther Banaian and Sunita Chepuri and Elizabeth Kelley and Sylvester W. Zhang},
journal= {arXiv preprint arXiv:2107.14785},
year = {2022}
}