发表机构
University of Science and Technology of China（中国科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了正空间上整体单项式的线性无关性，该方法基于洛朗展开的牛顿多面体研究，所得结果可应用于簇代数等相关代数，得到洛朗单项式性质及簇单项式线性无关性。
AI 中文摘要
本文证明了正空间上的整体单项式是线性无关的，该方法基于对洛朗展开的牛顿多面体的研究。我们的一般结果可应用于来自簇代数的正空间以及许多洛朗现象代数，进而得到洛朗展开的所谓真洛朗单项式性质，以及这类代数的簇单项式的线性无关性。
英文摘要
In this paper, we prove that global monomials on positive spaces are linearly independent, extending the basic fact that Laurent monomials in a Laurent polynomial algebra are linearly independent to a much more general setting. We also establish a global monomial avoidance phenomenon for positive spaces. Our approach is based on the study of Newton polytopes of Laurent expansions. These general results apply to positive spaces arising from cluster algebras (including the totally sign-skew-symmetric case), $Y$-patterns, and Laurent phenomenon algebras whose clusters are related by subtraction-free birational transformations. In particular, we obtain the proper Laurent monomial property and the linear independence of cluster monomials for all cluster algebras and Laurent phenomenon algebras under consideration. Notably, the proper Laurent monomial property follows from the global monomial avoidance phenomenon for positive spaces.
Comments17pages. Comments are welcome
