Congruences in slim, planar, \\semimodular lattices: The Swing Lemma
نویسندگان
چکیده
منابع مشابه
Notes on Planar Semimodular Lattices. Ii. Congruences
We show that in a finite semimodular lattice, the ordering of joinirreducible congruences is done in a special type of sublattice, we call a tight S7.
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A finite lattice L is called slim if no three join-irreducible elements of L form an antichain. Slim lattices are planar. Slim semimodular lattices play the main role in [3], where lattice theory is applied to a purely group theoretical problem. After exploring some easy properties of slim lattices and slim semimodular lattices, we give two visual structure theorems for slim semimodular lattices.
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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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Rectangular lattices are special planar semimodular lattices introduced by G. Grätzer and E. Knapp in 2009. By a patch lattice we mean a rectangular lattice whose weak corners are coatoms. As a sort of gluings, we introduce the concept of a patchwork system. We prove that every glued sum indecomposable planar semimodular lattice is a patchwork of its maximal patch lattice intervals “sewn togeth...
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ژورنال
عنوان ژورنال: Acta Scientiarum Mathematicarum
سال: 2015
ISSN: 0001-6969
DOI: 10.14232/actasm-015-757-1