Notes on planar semimodular lattices. IX. $\mathcal{C}_1$-diagrams

TL;DR

This paper proves the existence of a special diagram type for slim, planar, semimodular lattices, which are a particular class of mathematical structures with specific properties.

Contribution

It establishes the existence of Czédli's powerful diagram type for slim, planar, semimodular lattices, advancing the understanding of their visual representations.

Findings

Existence of Czédli's diagram type is proven.

The diagram type applies to slim, planar, semimodular lattices.

Enhances visualization and analysis of these lattices.

Abstract

A planar semimodular lattice $L$ is \emph{slim} if $\mathbf{M}_3$ is not a sublattice of $L$. In a recent paper, G. Cz\'edli introduced a very powerful diagram type for slim, planar, semimodular lattices. This short note proves the existence of such diagrams.