On the number of slim, semimodular lattices
نویسندگان
چکیده
منابع مشابه
Slim 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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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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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.
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Let ~ H and ~ K be finite composition series of a group G. The intersections Hi ∩ Kj of their members form a lattice CSL( ~ H, ~ K) under set inclusion. Improving the Jordan-Hölder theorem, G. Grätzer, J.B. Nation and the present authors have recently shown that ~ H and ~ K determine a unique permutation π such that, for all i, the i-th factor of ~ H is “down-and-up projective” to the π(i)-th f...
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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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ژورنال
عنوان ژورنال: Mathematica Slovaca
سال: 2016
ISSN: 1337-2211,0139-9918
DOI: 10.1515/ms-2015-0111