# Rooted Clusters for Graph LP Algebras

@article{Banaian2022RootedCF, title={Rooted Clusters for Graph LP Algebras}, author={Esther Banaian and Sunita Chepuri and Elizabeth Kelley and Sylvester W. Zhang}, journal={Symmetry, Integrability and Geometry: Methods and Applications}, year={2022} }

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…

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