The 1/3-2/3 Conjecture for ordered sets whose cover graph is a forest
Combinatorics
2017-06-20 v3
Abstract
A balanced pair in an ordered set is a pair of elements of such that the proportion of linear extensions of that put before is in the real interval . We define the notion of a good pair and claim any ordered set that has a good pair will satisfy the conjecture and furthermore every ordered set which is not totally ordered and has a forest as its cover graph has a good pair.
Cite
@article{arxiv.1610.00809,
title = {The 1/3-2/3 Conjecture for ordered sets whose cover graph is a forest},
author = {Imed Zaguia},
journal= {arXiv preprint arXiv:1610.00809},
year = {2017}
}