Results 231 to 240 of about 33,221 (269)

On the Lattice of Convex Sublattices of a Lattice

Southeast Asian Bulletin of Mathematics, 2003
In Algebra Univers. 35, 63-71 (1996; Zbl 0842.06003), \textit{S. Lavanya} and \textit{S. Parameshwara Bhatta} considered a partial ordering on the set \(\text{CS}(L)\) of all the convex sublattices of a lattice \(L\), namely \(A\leq B\) if and only if \((A]\subseteq (B]\) and \([A)\supseteq [B)\), and begun a corresponding study.
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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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Lattices of Games

Order, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michael Henry Albert, Richard J. Nowakowski   +1 more
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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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Viscous Lattices

Journal of Mathematical Imaging and Vision, 2005
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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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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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Excess of a Lattice

Graphs and Combinatorics, 2002
A pair \((x,y)\) of elements in a lattice is said to be mismatching if \(x\) is join-irreducible, \(y\) is meet-irreducible and \(x\nleqslant y\). The excess of a lattice \(L\) is the number \(\text{ex}(L) =|L|-\min \{|V_x|+ |I_y|\): \((x,y)\) is a mismatching pair\}, where \(V_x\) and \(I_y\) are the filter generated by \(x\) and the ideal generated ...
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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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