Notes on planar semimodular lattices. I. Construction

TL;DR

This paper presents a straightforward method to construct all planar semimodular lattices using three simple steps starting from the direct product of two chains.

Contribution

It introduces a novel, simplified construction process for all planar semimodular lattices from basic components.

Findings

All planar semimodular lattices can be generated through the proposed three-step process.

The construction method simplifies understanding and building these lattices.

Provides a foundation for further structural analysis of semimodular lattices.

Abstract

We construct all planar semimodular lattices in three simple steps from the direct product of two chains.