Planar semilattices and nearlattices with eighty-three subnearlattices
G\'abor Cz\'edli

TL;DR
This paper establishes a condition linking the number of subnearlattices in finite nearlattices to their planarity, providing a sharp threshold for when such structures have planar Hasse diagrams.
Contribution
It proves a sharp bound connecting the number of subnearlattices to the planarity of finite nearlattices, enriching the understanding of their structural properties.
Findings
Nearlattices with many subnearlattices are planar.
The bound of 83·2^{n-8} subnearlattices is sharp for n > 8.
Finite nearlattices are equivalent to several other algebraic structures.
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 -element nearlattice has at least subnearlattices, then it has a planar Hasse diagram. For , this result is sharp.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
