Another research note

Abstract

A planar semimodular lattice L is slim if 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, the C 1 -diagrams. Part IX provides a very short proof of the existence of C 1 -diagrams.In this part, we revisit the concept of natural diagrams I introduced with E. Knapp about a dozen years ago. Given a slim rectangular lattice L, we construct its natural diagram in one simple step. In this note, we show that for a slim rectangular lattice, a natural diagram is the same as a C 1 -diagram. This verifies that natural diagrams have all the nice properties of C 1 -diagrams.