On a result of Gábor Czédli concerning congruence lattices of planar semimodular lattices
نویسندگان
چکیده
منابع مشابه
Congruence Lattices of Finite Semimodular Lattices
We prove that every finite distributive lattice can be represented as the congruence lattice of a finite (planar) semimodular lattice.
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A recent result of G. Czédli and E. T. Schmidt gives a construction of slim (planar) semimodular lattices from planar distributive lattices by adding elements, adding “forks”. We give a construction that accomplishes the same by deleting elements, by “resections”.
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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...
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ژورنال
عنوان ژورنال: Acta Scientiarum Mathematicarum
سال: 2015
ISSN: 0001-6969
DOI: 10.14232/actasm-014-024-1