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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.
DOI: 10.14232/actasm-019-573-4
AMS Subject Classification
(1991): 06A12, 06B75, 20M10
Keyword(s):
planar nearlattice,
planar semilattice,
planar lattice,
chopped lattice,
number of subalgebras,
computer-assisted proof,
commutative idempotent semigroup
received 23.8.2019, revised 22.1.2020, accepted 29.1.2020. (Registered under 823/2019.)
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