Planar semilattices and nearlattices with eighty-three subnearlattices

2019/08/22 by Gábor Czédli, Czédli, Gábor
Mathematics · #06A12 #06B75 #20M10 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:06A12 #msc:06B75 #msc:20M10

paper · pdf · doi:10.48550/arxiv.1908.08155

71 pages, 7 figures

arxiv created 2019/08/22 · arxiv updated 2019/08/23

Abstract

Finite (upper) nearlattices are essentially the same mathematical entities as finite semilattices, finite commutative idempotent semigroups, finite join-enriched meet semilattices, and chopped lattices. We prove that if an n-element nearlattice has at least 83⋅ 2^n-8 subnearlattices, then it has a planar Hasse diagram. For n>8, this result is sharp.

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