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Flattening antichains with respect to the volume.

Brankovic, Ljiljana, Lieby, Paulette, Miller, Mirka (1999)

The Electronic Journal of Combinatorics [electronic only]

Frankl’s conjecture for large semimodular and planar semimodular lattices

Gábor Czédli, E. Tamás Schmidt (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

A lattice $L$ is said to satisfy (the lattice theoretic version of) Frankl’s conjecture if there is a join-irreducible element $f \in L$ such that at most half of the elements $x$ of $L$ satisfy $f \leq x$ . Frankl’s conjecture, also called as union-closed sets conjecture, is well-known in combinatorics, and it is equivalent to the statement that every finite lattice satisfies Frankl’s conjecture. Let $m$ denote the number of nonzero join-irreducible elements of $L$ . It is well-known that $L$ consists of at most $2^{m}$ elements....

Full embeddings into the categories of Boolean algebras

Věra Trnková (1986)

Commentationes Mathematicae Universitatis Carolinae

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Flattening antichains with respect to the volume.

Frankl’s conjecture for large semimodular and planar semimodular lattices

Full embeddings into the categories of Boolean algebras

Currently displaying 1 – 3 of 3