Results 281 to 290 of about 86,942 (318)

Lattice points in lattice polytopes

Mathematika, 2001
Let \(P\) be a lattice polytope in \(\mathbb{R}^d\) with vertices in \(\mathbb{Z}^d\), and \(I_l(P) = \operatorname{int}(P) \cap l \mathbb{Z}^d\) denote the set of sublattice points of \(P\) in its interior. Using and generalizing results of \textit{J. C. Lagarias} and \textit{G. M. Ziegler} [Can. J. Math. 43, No.
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Isometrical Embeddings of Lattices into Geometric Lattices

Order, 2012
Embedding lattices into geometric lattices gained substantial interest since the fundamental result of Dilworth on finite lattices. The nice paper under review elaborates on Dilworth's approach and shows that an algebraic lattices endowed with a pseudorank function and having all compact elements of finite height does admit an isometric embedding into ...
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Viscous Lattices

Journal of Mathematical Imaging and Vision, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Lattices of Uniformities

Order, 2007
The author studies lattice-theoretical properties of lattices of uniformities, such as modularity, distributive laws and the existence of (relative) complements. In these investigations the concept of permutable uniformities turns out to be useful: Two uniformities \(u,v\) on a set \(X\) are said to be permutable if \(v\circ u = u\circ v\) where \(u ...
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Lattices of Games

Order, 2011
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Michael Henry Albert, Richard J. Nowakowski   +1 more
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On the sublattice-lattice of a lattice

Algebra Universalis, 1984
A property P of algebras in any variety V might be called S-determined if when A has P and A, A' have isomorphic lattices of subalgebras. A' has P; S-sharp if the same conditions imply \(A'=F(A)\) for some automorphism F of V. The authors show that being a pseudocomplemented lattice of finite length is S-determined, and produce two new S-sharp ...
Chen, C.C., Koh, K.M., Teo, K.L.
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On the sublattice-lattices of lattices

Publicationes Mathematicae Debrecen, 1998
For a lattice \(L\), let \(\text{Sub}(L)\) denote the lattice of all sublattices of \(L\), and \(L^d\) the dual of \(L\). If \(L\) and \(K\) are lattices and \(L\approx K\) or \(L\approx K^d\), then \(\text{Sub}(L)\approx \text{Sub}(K)\). The converse in not true in general. The scope of this paper is to prove that if \(L\) and \(K\) are lattices with \
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On congruence lattices of lattices

Algebra Universalis, 1985
This paper concerns the old problem, whether every distributive algebraic lattice is isomorphic to the congruence lattice of a lattice. The author discovers a new approach to reduce the representation problem to investigations of congruence lattices of finite lattices. His approach is the following. Let D be the category of finite distributive lattices
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Lattices of lattice homomorphisms

Algebra Universalis, 1978
IfL andM are lattices, Hom (L, M) denotes the set of homomorphisms ofL intoM with the pointwise partial order.L is calledcatalytic if Hom (L, M) is a lattice for every latticeM. Among other results, it is shown that every retract of a lattice completely freely generated by a partially ordered set is catalytic, and that every catalytic lattice is ...
Kucera, T. G., Sands, B.
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Congruence Lattices of Finite Lattices as Concept Lattices

1990
In formal concept analysis it is of increasing interest to compute and to represent congruence lattices of finite lattices (for instance, to assist adequate drawings of concept lattices). In this note we give a representation of such congruence lattices as concept lattices which allows the use of developed computer programs to determine and to draw ...
Sigrid Knecht, Rudolf Wille
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