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