Zilber's Theorem for planar lattices, revisited
Kirby A. Baker, George Gr\"atzer
TL;DR
This paper revisits Zilber's Theorem, providing a new proof that finite planar lattices are characterized by the existence of a complementary order relation, and explores applications like canonical forms and coverings.
Contribution
It offers a novel proof of Zilber's Theorem and discusses applications such as canonical forms and analysis of coverings in finite planar lattices.
Findings
New proof of Zilber's Theorem for finite lattices
Canonical form for finite planar lattices
Analysis of coverings in the left-right order
Abstract
Zilber's Theorem states that a finite lattice is planar if{}f 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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Logic · semigroups and automata theory