One Hundred Twenty-Seven Subsemilattices and Planarity-Reference-Cited by-同舟云学术

One Hundred Twenty-Seven Subsemilattices and Planarity

Published:2019-12-18 Issue:3 Volume:37 Page:559-569
ISSN:0167-8094
Container-title:Order
language:en
Short-container-title:Order

Author:

Czédli Gábor^ORCID

Abstract

AbstractLet L be a finite n-element semilattice. We prove that if L has at least 127 ⋅ 2n− 8 subsemilattices, then L is planar. For n > 8, this result is sharp since there is a non-planar semilattice with exactly 127 ⋅ 2n− 8 − 1 subsemilattices.

Funder

Nemzeti Kutatási Fejlesztési és Innovációs Hivatal

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,Geometry and Topology,Algebra and Number Theory

Link

http://link.springer.com/content/pdf/10.1007/s11083-019-09519-x.pdf

Reference10 articles.

1. Ahmed, D., Horváth, E.K.: Yet two additional large numbers of subuniverses of finite lattices, Discussiones Mathematicae—General Algebra and Applications, to appear

2. Chajda, I., Czédli, G., Rosenberg, I.G.: On lattices whose ideals are all tolerance kernels. Acta Sci. Math. (Szeged) 61, 23–32 (1995)

3. Czédli, G.: A note on finite lattices with many congruences. Acta Universitatis Matthiae Belii, Series Mathematics Online, 22–28. http://actamath.savbb.sk/oacta2018003.shtml (2018)

4. Czédli, G.: Lattices with many congruences are planar. Algebra Universalis 80, 16 (2019)

5. Czédli, G.: Finite semilattices with many congruences. Order 36, 233–247 (2019)

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