Planar semilattices and nearlattices with eighty-three subnearlattices

DOI10.14232/ACTASM-019-573-4zbMATH Open1474.06009arXiv1908.08155OpenAlexW3024614199MaRDI QIDQ5126102

Gábor Czédli

Publication date: 2 October 2020

Published in: Acta Scientiarum Mathematicarum (Search for Journal in Brave)

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 $83cdot{2}^{n-8}$ subnearlattices, then it has a planar Hasse diagram. For $n>8$, this result is sharp.

Full work available at URL: https://arxiv.org/abs/1908.08155

zbMATH Keywords

computer-assisted proofplanar latticechopped latticeplanar semilatticenumber of subalgebrascommutative idempotent semigroupplanar nearlattice

Mathematics Subject Classification ID

General structure theory for semigroups (20M10) Semilattices (06A12) Generalizations of lattices (06B75)

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