Eighty-three sublattices and planarity

2019/01/03 by Gábor Czédli, Czédli, Gábor
Mathematics · #06B99 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06B99

paper · pdf · doi:10.48550/arxiv.1901.00572

100 pages, 5 figures

arxiv created 2019/07/02 · arxiv updated 2019/07/03

Abstract

Let L be a finite n-element lattice. We prove that if L has at least 83⋅ 2^n-8 sublattices, then L is planar. For n>8, this result is sharp since there is a non-planar lattice with exactly 83⋅ 2^n-8-1 sublattices.

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