Notes on planar semimodular lattices. VII. Resections of planar semimodular lattices

TL;DR

This paper introduces a new method called resections for constructing slim planar semimodular lattices from planar distributive lattices, complementing existing methods that add elements.

Contribution

It presents a novel resection technique for building slim planar semimodular lattices through element deletion, expanding the toolkit beyond the existing 'fork' addition method.

Findings

Resections effectively construct slim planar semimodular lattices.

Resections provide an alternative to the 'fork' addition method.

The method broadens understanding of lattice construction techniques.

Abstract

A recent result of G. Cz\'edli and E.\,T. Schmidt gives a construction of slim (planar) semimodular lattices from planar distributive lattices by adding elements, adding "forks". We give a construction that accomplishes the same by deleting elements, by "resections".