Counting linear extensions of restricted posets
Combinatorics
2018-02-20 v1
Abstract
The classical 1991 result by Brightwell and Winkler states that the number of linear extensions of a poset is #P-complete. We extend this result to posets with certain restrictions. First, we prove that the number of linear extension for posets of height two is #P-complete. Furthermore, we prove that this holds for incidence posets of graphs. Finally, we prove that the number of linear extensions for posets of dimension two is #P-complete.
Cite
@article{arxiv.1802.06312,
title = {Counting linear extensions of restricted posets},
author = {Samuel Dittmer and Igor Pak},
journal= {arXiv preprint arXiv:1802.06312},
year = {2018}
}