ACTA issues

Zilber's Theorem for planar lattices, revisited

Kirby A. Baker, George Gr├Ątzer

Acta Sci. Math. (Szeged) 86:1-2(2020), 81-104

Abstract. Zilber's Theorem states that a finite lattice $L$ is planar if and only if it has a complementary order relation. We provide a new proof for this crucial result and discuss some applications, including a canonical form for finite planar lattices and an analysis of coverings in the left-right order.

DOI: 10.14232/actasm-019-230-9

AMS Subject Classification (1991): 06C10, 06A07

Keyword(s): planar lattice, Zilber's Theorem

received 30.7.2019, revised 22.1.2020, accepted 29.1.2020. (Registered under 730/2019.)