Cluster algebras and binary subwords
arXiv:1910.07611 · doi:10.1007/s11083-021-09562-7
Abstract
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.
15 pages, 13 figures
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