Geodesic
Rooted Clusters for Graph LP Algebras
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $T$-paths.
Keywords: Laurent phenomenon algebra, cluster algebra, graph LP algebra, $T$-path. 
@article{SIGMA_2022_18_a88,
     author = {Esther Banaian and Sunita Chepuri and Elizabeth Kelley and Sylvester W. Zhang},
     title = {Rooted {Clusters} for {Graph} {LP} {Algebras}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a88/}
}
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Esther Banaian; Sunita Chepuri; Elizabeth Kelley; Sylvester W. Zhang. Rooted Clusters for Graph LP Algebras. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a88/

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