Geodesic
The Canonical Join Complex for Biclosed Sets
Séminaire lotharingien de combinatoire, 80B (2018)

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The canonical join complex of a semidistributive lattice is a simplicial complex whose faces are canonical join representations of elements of the semidistributive lattice. We give a combinatorial classification of the faces of the canonical join complex of the lattice of biclosed sets of segments supported by a tree, as introduced by the third author and McConville. We also use our classification to describe the elements of the shard intersection order of the lattice of biclosed sets. As a consequence, we prove that this shard intersection order is a lattice. 

@article{SLC_2018_80B_a1,
     author = {Alexander Clifton and Peter Dillery, and Alexander Garver},
     title = {The {Canonical} {Join} {Complex} for {Biclosed} {Sets}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a1/}
}
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AU  - Alexander Garver
TI  - The Canonical Join Complex for Biclosed Sets
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
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%A Peter Dillery,
%A Alexander Garver
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%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a1/
%F SLC_2018_80B_a1
Alexander Clifton; Peter Dillery,; Alexander Garver. The Canonical Join Complex for Biclosed Sets. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a1/