Semimodular Lattices Theory and Applications
نویسنده
چکیده
Stern, Manfred. Semimodular lattices: theory and applications. / Manfred Stern. p. cm. – (Encyclopedia of mathematics and its applications ; v. 73) Includes bibliographical references and index.
منابع مشابه
Frankl's Conjecture for a subclass of semimodular lattices
In this paper, we prove Frankl's Conjecture for an upper semimodular lattice $L$ such that $|J(L)setminus A(L)| leq 3$, where $J(L)$ and $A(L)$ are the set of join-irreducible elements and the set of atoms respectively. It is known that the class of planar lattices is contained in the class of dismantlable lattices and the class of dismantlable lattices is contained in the class of lattices ha...
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.
متن کاملFinite Lattices and Jordan-holder Sets 1)
In this paper we extend some aspects of the theory of 'supersolvable lattices' [3] to a more general class of finite lattices which includes the upper-semimodular lattices. In particular, all conjectures made in [33 concerning upper-semimodular lattices will be proved. For instance, we will prove that if L is finite upper-semimodular and if L' denotes L with any set of 'levels' removed, then th...
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”.
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...
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