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arXiv · 1908.08155

Planar semilattices and nearlattices with eighty-three subnearlattices

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

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Gábor Czédli. 2019-08-22. Planar semilattices and nearlattices with eighty-three subnearlattices. https://arxiv.org/abs/1908.08155

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