Note on antichain cutsets in discrete semimodular lattices

TL;DR

This paper extends the characterization of level sets as antichain cutsets from finite Boolean lattices to all discrete semimodular lattices, broadening the understanding of lattice structures.

Contribution

It generalizes a known property of Boolean lattices to a wider class of discrete semimodular lattices, providing new insights into their structure.

Findings

Level sets are antichain cutsets in all discrete semimodular lattices.

The characterization previously known for Boolean lattices applies more broadly.

The result enhances the theoretical understanding of lattice theory.

Abstract

The characterization of level sets of finite Boolean lattices as antichain cutsets, due to Rival and Zaguia, is seen to hold in all discrete semimodular lattices.