Theses of Ph.D. Dissertation Modular and semimodular lattices
نویسندگان
چکیده
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...
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In a ranked lattice, we consider two maximal chains, or “flags” to be i-adjacent if they are equal except possibly on rank i . Thus, a finite rank lattice is a chamber system. If the lattice is semimodular, as noted in [9], there is a “Jordan-Hölder permutation” between any two flags. This permutation has the properties of an Sn-distance function on the chamber system of flags. Using these noti...
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Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold [6] developed an algorithm to enumerate, up to isomorphism, all nite lattices up to size 18. Here we adapt and improve this algorithm to construct and count modular lattices up to size 23, semimodular lattices up to size 22, and lattices of size 19. ...
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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...
متن کاملGenerating all nite modular lattices of a given size
Modular lattices, introduced by R. Dedekind, are an important subvariety of lattices that includes all distributive lattices. Heitzig and Reinhold [6] developed an algorithm to enumerate, up to isomorphism, all nite lattices up to size 18. Here we adapt and improve this algorithm to construct and count modular lattices up to size 23, semimodular lattices up to size 22, and lattices of size 19. ...
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تاریخ انتشار 2013