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Frankl’s conjecture for large semimodular and planar semimodular lattices

Gábor CzédliE. 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 L such that at most half of the elements x of L satisfy f 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....

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