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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