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

Abstract

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