8 papers · 1 filter
Lattices with many congruences are planar
Gábor Czédli
Let be an -element finite lattice. We prove that if has strictly more than congruences, then is planar. This result is sharp, since for each natural number…
Symmetric embeddings of free lattices into each other
Gábor Czédli, Gergő Gyenizse, Ádám Kunos
By a 1941 result of Ph. M. Whitman, the free lattice FL(3) on three generators includes a sublattice that is isomorphic to the lattice FL()=FL() generated freely b…
Finite semilattices with many congruences
Gábor Czédli
For an integer , let NCSL denote the set of sizes of congruence lattices of -element semilattices. We find the four largest numbers belonging to NCSL, provide…
Characterizing fully principal congruence representable distributive lattices
Gábor Czédli
Motivated by a recent paper of G. Grätzer, a finite distributive lattice is said to be fully principal congruence representable if for every subset of containing , $…
Quasiplanar diagrams and slim semimodular lattices
Gábor Czédli
A (Hasse) diagram of a finite partially ordered set (poset) P will be called quasiplanar if for any two incomparable elements u and v, either v is on the left of all maximal chains…
Distributive lattices determined by weighted double skeletons
Gábor Czédli, Joanna Grygiel, Katarzyna Grygiel
Related to his S-glued sum construction, the skeleton S(L) of a finite lattice L was introduced by C. Herrmann in 1973. Our theorem asserts that if D is a finite distributive latti…