ACTA issues

Atom-generated planar lattices

G. Gr├Ątzer

Acta Sci. Math. (Szeged) 86:3-4(2020), 351-357

Abstract. In this note, we discuss planar lattices generated by their atoms. We prove that if $L$ is a planar lattice generated by $n$ atoms, then both the left and the right boundaries of $L$ have at most $n+1$ elements. On the other hand, $L$ can be arbitrarily large. For every $k > 1$, we construct a planar lattice $L$ generated by $4$ atoms such that $L$ has more than $k$ elements.

DOI: 10.14232/actasm-020-363-7

AMS Subject Classification (1991): 06B05

Keyword(s): planar, atom-generated

received 13.1.2019, revised 3.9.2020, accepted 4.9.2020. (Registered under 113/2020.)