The Asymptotic Number of Planar, Slim, Semimodular Lattice Diagrams
نویسندگان
چکیده
منابع مشابه
The Matrix of a Slim Semimodular Lattice
A finite lattice L is called slim if no three join-irreducible elements of L form an antichain. Slim semimodular lattices play the main role in G. Czédli and E.T. Schmidt [5], where lattice theory is applied to a purely group theoretical problem. Here we develop a unique matrix representation for these lattices.
متن کاملSlim Semimodular Lattices. I. A Visual Approach
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...
متن کاملSlim Semimodular Lattices. II. A Description by Patchwork Systems
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...
متن کاملNotes on Planar Semimodular Lattices. VII. Resections of Planar Semimodular Lattices
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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ژورنال
عنوان ژورنال: Order
سال: 2015
ISSN: 0167-8094,1572-9273
DOI: 10.1007/s11083-015-9361-0