Geodesic
Dual Equivalence Graphs and CAT(0) Combinatorics
Séminaire lotharingien de combinatoire, 80B (2018)

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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. 

@article{SLC_2018_80B_a91,
     author = {Anastasia Chavez and John Guo},
     title = {Dual {Equivalence} {Graphs} and {CAT(0)} {Combinatorics}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a91/}
}
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AU  - Anastasia Chavez
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TI  - Dual Equivalence Graphs and CAT(0) Combinatorics
JO  - Séminaire lotharingien de combinatoire
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VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a91/
ID  - SLC_2018_80B_a91
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%A John Guo
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%J Séminaire lotharingien de combinatoire
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%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a91/
%F SLC_2018_80B_a91
Anastasia Chavez; John Guo. Dual Equivalence Graphs and CAT(0) Combinatorics. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a91/