a new property of congruence lattices of slim, planar, semimodular lattices

the systematic study of planar semimodular lattices started in 2007 with a series of papers by g. gr¨atzer and e. knapp. these lattices have connections with group theory and geometry. a planar semimodular lattice l is slim if m3 it is not a sublattice of l. in his 2016 monograph, “the congruences of a finite lattice, a proof-by-picture approach”, the second author asked for a characterization of congruence lattices of slim, planar, semimodular lattices. in addition to distributivity, both authors have previously found specific properties of these congruence lattices. in this paper, we present a new property, the three-pendant three-crown property. the proof is based on the first author’s papers: 2014 (multifork extensions), 2017 (c1-diagrams), and a recent paper (lamps), introducing the tools we need.