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Finite Dismantlable Semidistributive Lattices are Planar

2015/01/12 by Henri Mühle, Mühle, Henri
Mathematics · #06B05 (Primary) #06D15 #06D75 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:06B05 #msc:06D15 #msc:06D75

paper · pdf · doi:10.48550/arxiv.1501.02617

This article was withdrawn, because I was notified of a counterexample to Theorem 1.1, and that Theorem 1.2 has appeared in the literature before

arxiv created 2015/07/02 · arxiv updated 2015/07/03

Abstract

In this article, we prove that finite semidistributive lattices are dismantlable if and only if they are planar. This extends a well-known result by Kelly and Rival that states the same property for finite distributive lattices. Moreover, we show how the breadth of finite semidistributive lattices can be computed with the help of canonical join representations. We use this result to conclude that the breadth of a finite semidistributive dismantlable lattice cannot exceed 2.

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