On a Property of Congruence Lattices of Slim, Planar, Semimodular Lattices

Abstract

In a 2121 paper with G´abor Cz´edli, we introduced and verified the Three-pendant Three-crown Property, 3P3C, for congruence lattices of slim (no M3 sublattice), planar, semimodular lattices. The proof is very long; in part, because it relies on Cz´edli’s 2021 paper on lamps. This paper verifies 3P3C using the Swing Lemma, an elementary and short approach. 2020 Mathematics Subject Classification. 06C10.