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Bailey, Rachel; Gunawan, Emily

Cluster algebras and binary subwords. (English) Zbl 1520.13032

Order 39, No. 1, 55-69 (2022).
Summary: 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 \(G\).

Cited in 1 Document

MSC:

13F60 Cluster algebras
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
06A07 Combinatorics of partially ordered sets
68R15 Combinatorics on words

Keywords:

snake graph perfect matching; cluster algebra; binary subword; binomial coefficient of words; antichain; order filter; piecewise-linear poset; fence poset; path poset
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References:

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