2009•arXiv (Cornell University)Open access

Linear Extension Diameter of Downset Lattices of 2-Dimensional Posets

Stefan Felsner, Mareike Massow

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|.

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Key concepts: Extension (predicate logic), Linear extension, Mathematics, Pure mathematics, Combinatorics, Geometry, Computer science, Partially ordered set