The canonical join complex for biclosed sets
Combinatorics
2017-10-02 v5
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.
Cite
@article{arxiv.1708.02580,
title = {The canonical join complex for biclosed sets},
author = {Alexander Clifton and Peter Dillery and Alexander Garver},
journal= {arXiv preprint arXiv:1708.02580},
year = {2017}
}
Comments
preliminary version, comments welcome; in v3, more examples and figures; in v4, corrections; in v5, fixed error in Theorem 4.1