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The linear extension diameter of a finite poset P is the maximum distancebetween a pair of linear extensions of P, where the distance between two linearextensions is the number of pairs of elements of P appearing in differentorders in the two linear extensions. We prove a formula for the linearextension diameter of the Boolean Lattice and characterize the diametral pairsof linear extensions. For the more general case of a downset lattice D_P of a2-dimensional poset P, we characterize the diametral pairs of linear extensionsof D_P and show how to compute the linear extension diameter of D_P in timepolynomial in |P|.

Linear Extension Diameter of Downset Lattices of 2-Dimensional Posets