English

Linear Extension Diameter of Downset Lattices of 2-Dimensional Posets

Combinatorics 2009-07-13 v1

Abstract

The linear extension diameter of a finite poset P is the maximum distance between a pair of linear extensions of P, where the distance between two linear extensions is the number of pairs of elements of P appearing in different orders in the two linear extensions. We prove a formula for the linear extension diameter of the Boolean Lattice and characterize the diametral pairs of linear extensions. For the more general case of a downset lattice D_P of a 2-dimensional poset P, we characterize the diametral pairs of linear extensions of D_P and show how to compute the linear extension diameter of D_P in time polynomial in |P|.

Keywords

Cite

@article{arxiv.0907.1793,
  title  = {Linear Extension Diameter of Downset Lattices of 2-Dimensional Posets},
  author = {Stefan Felsner and Mareike Massow},
  journal= {arXiv preprint arXiv:0907.1793},
  year   = {2009}
}

Comments

25 pages, 7 figures