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<p>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 <i>T</i>-path.</p>

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Hydra Graphs for Graph LP Algebras

  • 期刊论文

  • 发表日期：

    2025年12月19日

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  • Esther Banaian,
  • Sunita Chepuri,
  • Elizabeth Kelley,
  • Sylvester W. Zhang

摘要

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 T-path.