Strong semimodular lattices and Frankl's conjecture
Frankl's conjecture says that in every nontrivial finite lattice \(L\) there is a join-irreducible element \(a\) such that the principal filter \(F(a)\) has at most \(|L|/2\) elements. It is known that this conjecture holds for lower semimodular or section-complemented lattices, but it is unknown whether it holds for upper semimodular lattices. The author introduces the concept of a strong semimodular lattice and proves Frankl's conjecture for these lattices.
scientific article; zbMATH DE number 1899975