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arXiv · 2608.30907

Linear independence of global monomials on positive spaces

Peigen Cao
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Abstract

In this paper, we prove that the global monomials on positive spaces are linearly independent. The approach is based on the study of the Newton polytopes of Laurent expansions. Our general results can be applied to the positive spaces arising from cluster algebras and many Laurent phenomenon algebras, which in turn yield the so-called proper Laurent monomial property of Laurent expansions and the linear independence of cluster monomials for such algebras.

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Peigen Cao. 2026-08-31. Linear independence of global monomials on positive spaces. https://arxiv.org/abs/2608.30907

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