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Institute for Advanced Study（高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了Lam和Pylyavskyy提出的猜想：对于所有无环且无重边的有向图，任意种子簇下每个簇变量的Laurent展开式系数均为非负。
AI 中文摘要
Laurent现象代数由Lam和Pylyavskyy引入，作为簇代数的一般化。对于与有向图相关的一族代数，他们证明了每个簇变量都是任意簇中变量的Laurent多项式，并猜想这些展开式具有非负系数。我们证明了对于所有无环且无重边的有向图，相对于任意种子簇，该猜想成立。
英文摘要
Laurent phenomenon algebras were introduced by Lam and Pylyavskyy as a generalisation of cluster algebras. For a family associated with directed graphs, they showed that every cluster variable is a Laurent polynomial in the variables of any cluster and conjectured that these expansions have nonnegative coefficients. We prove this conjecture for all directed graphs without loops or multiple edges with respect to an arbitrary seed cluster.
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