7 papers
Large filters of quasiorder lattices can be generated by few elements
Gábor Czédli
For a poset , the quasiorders (AKA preorders) extending the poset order "" form a complete lattice , which is a filter in the lattice of all quasiorders of the s…
Reducing the lengths of slim planar semimodular lattices without changing their congruence lattices
Gábor Czédli
Following G. Grätzer and E. Knapp (2007), a slim semimodular lattice, SPS lattice for short, is a finite planar semimodular lattice having no as a sublattice. An SPS lattice…
Notes on congruence lattices and lamps of slim semimodular lattices
Gábor Czédli
Since their introduction by G. Grätzer and E. Knapp in 2007, more than four dozen papers have been devoted to finite slim planar semimodular lattices (in short, SPS lattices or sli…
Lattices with lots of congruence energy
Gábor Czédli
In 1978, motivated by E. Hückel's work in quantum chemistry, I. Gutman introduced the concept of the energy of a finite simple graph as the sum of the absolute values of the ei…
2-distributivity and lattices of sublattices closed under taking relative complements
Gábor Czédli
For a modular lattice of finite length, we prove that the distributivity of is a sufficient condition while its 2-distributivity is a necessary condition that those sublatt…
Retracts of rectangular distributive lattices and some related observations
Gábor Czédli
By a rectangular distributive lattice we mean the direct product of two non-singleton finite chains. We prove that the retracts (ordered by set inclusion and together with the empt…
A property of meets in slim semimodular lattices and its application to retracts
Gábor Czédli
Slim semimodular lattices were introduced by G. Grätzer and E. Knapp in 2007, and they have intensively been studied since then. It is often reasonable to give these lattices by th…