This paper establishes a connection between binary subwords and perfect matchings of a snake graph, an important tool in the theory of cluster algebras. Every binary expansion w can be associated to a piecewise-linear poset P and a snake graph G. We construct a tree structure called the antichain trie which is isomorphic to the trie of subwords introduced by Leroy, Rigo, and Stipulanti. We then present bijections from the subwords of w to the antichains of P and to the perfect matchings of G.

中文翻译：

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簇代数和二进制子词

本文建立了二进制子词与蛇形图的完美匹配之间的联系，蛇形图是聚类代数理论中的重要工具。每个二元展开w可以与分段线性波状图P和蛇形图G关联。我们构造了一个树结构，称为反链trie，它与Leroy，Rigo和Stipulanti引入的子词的trie同构。然后，我们介绍从w的子词到P的反链以及G的完美匹配的双射。