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arXiv · 0907.1793

Linear Extension Diameter of Downset Lattices of 2-Dimensional Posets

Stefan Felsner·Mareike Massow
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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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Stefan Felsner, Mareike Massow. 2009-07-10. Linear Extension Diameter of Downset Lattices of 2-Dimensional Posets. https://arxiv.org/abs/0907.1793

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