Finite Dismantlable Semidistributive Lattices are Planar
Combinatorics
2015-07-03 v2
Abstract
In this article, we prove that finite semidistributive lattices are dismantlable if and only if they are planar. This extends a well-known result by Kelly and Rival that states the same property for finite distributive lattices. Moreover, we show how the breadth of finite semidistributive lattices can be computed with the help of canonical join representations. We use this result to conclude that the breadth of a finite semidistributive dismantlable lattice cannot exceed .
Keywords
Cite
@article{arxiv.1501.02617,
title = {Finite Dismantlable Semidistributive Lattices are Planar},
author = {Henri Mühle},
journal= {arXiv preprint arXiv:1501.02617},
year = {2015}
}
Comments
This article was withdrawn, because I was notified of a counterexample to Theorem 1.1, and that Theorem 1.2 has appeared in the literature before