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arXiv · 1708.02580

The canonical join complex for biclosed sets

Alexander Clifton·Peter Dillery·Alexander Garver
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Abstract

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.

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Alexander Clifton, Peter Dillery, Alexander Garver. 2017-09-29. The canonical join complex for biclosed sets. https://arxiv.org/abs/1708.02580

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