Gábor Czédli

Weakly independent subsets in lattices

D E F I N I T I O N . A subset H of a lattice L is called weakly independent iff for all h, hl, h2 . . . . . h ~ e H which satisfy h < h l v h 2 v . . . v h , there exists an i (1--<i-< n) such that h-<h~. A maximal weakly independent set is called a basis of L. Every subchain of L is a weakly independent subset and any maximal chain is a basis. In this paper L denotes a finite distributive lattice and let Jo(L) denote the set of all join-irreducible elements of L. By using L e m m a 1 (cf. later) it is easy to show that Jo(L) is a basis of L.

On the Scope of Averaging for Frankl's Conjecture

Let

On tolerance lattices of algebras in congruence modular varieties

\mathcal F

Note on the description of join-distributive lattices by permutations

be a union-closed family of subsets of an m-element set A. Let

Quasiplanar Diagrams and Slim Semimodular Lattices

n=|{\mathcal F}|\ge 2

Lattice generation of small equivalences of a countable set

. For b ∈ A let w(b) denote the number of sets in

Finite Semilattices with Many Congruences

\mathcal F

Characterizing fully principal congruence representable distributive lattices

containing b minus the number of sets in

Large Sets of Lattices without Order Embeddings

\mathcal F

Sums of Lattices and a Relational Category

not containing b. Frankl’s conjecture from 1979, also known as the union-closed sets conjecture, states that there exists an element b ∈ A with w(b) ≥ 0. The present paper deals with the average of the w(b), computed over all b ∈ A.