ACTA issues

Planar semilattices and nearlattices with eighty-three subnearlattices

Gábor Czédli

Acta Sci. Math. (Szeged) 86:1-2(2020), 117-165

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.)