Séminaire Lotharingien de Combinatoire, 80B.92 (2018), 12 pp.

Anastasia Chavez and John Guo

Dual Equivalence Graphs and CAT(0) Combinatorics

Abstract. In this paper we explore the combinatorial structure of dual equivalence graphs Gλ. The vertices are Standard Young tableaux of a fixed shape λ that allows us to further understand the combinatorial structure of Gλ, and the edges are given by dual Knuth equivalences. The graph Gλ is the 1-skeleton of a cubical complex Cλ, and one can ask whether the cubical complex is CAT(0); this is a desirable metric property that allows us to describe the combinatorial structure of Gλ very explicitly. We prove that Cλ is CAT(0) if and only if λ is a hook.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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