The Number of Plane Diagrams of a Lattice

摘要

In this work we want to clarify, how many non-similar plane diagrams a planar lattice can have. In the first part demonstrate how to find all these diagrams by specifying all realizers, i.e. all pairs of linear orders whose intersection equals to the lattice order. The tools we use to achieve that goal are Ferrers-graphs [DDF84, Reu89] and left-relations on contexts [Zsc07]. Finally we determine the set of numbers which can occur as the number of plane diagrams of a planar lattice.