English

The 1/3-2/3 conjecture for $N$-free ordered sets

Combinatorics 2012-05-22 v2

Abstract

A balanced pair in a finite ordered set P=(V,)P=(V,\leq) is a pair (x,y)(x,y) of elements of VV such that the proportion of linear extensions of PP that put xx before yy is in the real interval [1/3,2/3][1/3, 2/3]. We prove that every finite NN-free ordered set which is not totally ordered has a balanced pair.

Keywords

Cite

@article{arxiv.1107.5626,
  title  = {The 1/3-2/3 conjecture for $N$-free ordered sets},
  author = {Imed Zaguia},
  journal= {arXiv preprint arXiv:1107.5626},
  year   = {2012}
}
R2 v1 2026-06-21T18:43:14.348Z