Temat: semimodular lattice - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: On interval decomposition lattices
Autorzy:: Foldes, Stephan
Radeleczki, Sándor
Powiązania:: https://bibliotekanauki.pl/articles/728916.pdf
Data publikacji:: 2004
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: interval
closure system
modular decomposition
semimodular lattice
partition lattice
strong set
lexicographic sum
Opis:: Intervals in binary or n-ary relations or other discrete structures generalize the concept of interval in an ordered set. They are defined abstractly as closed sets of a closure system on a set V, satisfying certain axioms. Decompositions are partitions of V whose blocks are intervals, and they form an algebraic semimodular lattice. Lattice-theoretical properties of decompositions are explored, and connections with particular types of intervals are established.
Źródło:: Discussiones Mathematicae - General Algebra and Applications; 2004, 24, 1; 95-114
1509-9415
Pojawia się w:: Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Finite orders and their minimal strict completion lattices
Autorzy:: Bordalo, Gabriela
Monjardet, Bernard
Powiązania:: https://bibliotekanauki.pl/articles/728964.pdf
Data publikacji:: 2003
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: atomistic lattice
join-irreducible element
distributive lattice
modular lattice
lower semimodular lattice
Dedekind-MacNeille completion
strict completion
weak order.
Opis:: Whereas the Dedekind-MacNeille completion D(P) of a poset P is the minimal lattice L such that every element of L is a join of elements of P, the minimal strict completion D(P)∗ is the minimal lattice L such that the poset of join-irreducible elements of L is isomorphic to P. (These two completions are the same if every element of P is join-irreducible). In this paper we study lattices which are minimal strict completions of finite orders. Such lattices are in one-to-one correspondence with finite posets. Among other results we show that, for every finite poset P, D(P)∗ is always generated by its doubly-irreducible elements. Furthermore, we characterize the posets P for which D(P)∗ is a lower semimodular lattice and, equivalently, a modular lattice.
Źródło:: Discussiones Mathematicae - General Algebra and Applications; 2003, 23, 2; 85-100
1509-9415
Pojawia się w:: Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:: Biblioteka Nauki

Artykuł

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