Séminaire Lotharingien de Combinatoire, 82B.81 (2019), 12 pp.

Rachel Bailey and Emily Gunawan

Cluster algebras and binary words

Abstract. We establish 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 describe bijections from the subwords of w to the antichains of P and to the perfect matchings of G. We also construct a tree structure called the antichain trie which is isomorphic to the trie of subwords introduced by Leroy, Rigo, and Stipulanti.

Received: November 15, 2018. Accepted: February 17, 2019. Final version: April 1, 2019.

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