Planar Posets that are Accessible from Below Have Dimension at Most 6
Combinatorics
2019-06-20 v1
Abstract
Planar posets can have arbitrarily large dimension. However, a planar poset of height has dimension at most , while a planar poset with minimal elements has dimension at most . In particular, a planar poset with a unique minimal element has dimension at most . In this paper, we extend this result by showing that a planar poset has dimension at most if it has a plane diagram in which every minimal element is accessible from below.
Cite
@article{arxiv.1906.08145,
title = {Planar Posets that are Accessible from Below Have Dimension at Most 6},
author = {Csaba Biró and Bartłomiej Bosek and Heather C. Smith and William T. Trotter and Ruidong Wang and Stephen J. Young},
journal= {arXiv preprint arXiv:1906.08145},
year = {2019}
}