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SUBLATTICES OF LATTICES OF ORDER-CONVEX SETS, III: THE CASE OF TOTALLY ORDERED SETS [PDF]
International Journal of Algebra and Computation, 2004 For a partially ordered set P, let Co(P) denote the lattice of all order-convex subsets of P. For a positive integer n, we denote by [Formula: see text] (resp., SUB(n)) the class of all lattices that can be embedded into a lattice of the form [Formula: see text] where <Ti|i∈I> is a family of chains (resp., chains with at most n elements).
Marina V. Semenova, Friedrich Wehrung
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Characterization problems for graphs, partially ordered sets, lattices, and families of sets
Discrete Mathematics, 1976 A standard problem in combinatorial theory is to characterize structures which satisfy a certain property by providing a minimum list of forbidden substructures, for example, Kuratowski's well known characterization of planar graphs. In this paper, we establish connections between characterization problems for interval graphs, circular are graphs ...
William T. Trotter, John I. Moore Jr.
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Dualization in lattices given by ordered sets of irreducibles
Theoretical Computer Science, 2017 Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and join irreducibles (i.e., as a concept lattice of a formal context).
Mikhail A. Babin, Sergei O. Kuznetsov
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The ordered set of principal congruences of a countable lattice [PDF]
Algebra universalis, 2016 For a lattice L, let Princ L denote the ordered set of principal congruences of L. In a pioneering paper, G. Gratzer characterized the ordered sets Princ L of finite lattices L; here we do the same for countable lattices. He also showed that each bounded ordered set H is isomorphic to Princ L of a bounded lattice L.
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Ordered Sets and Complete Lattices
, 2002 These notes deal with an interconnecting web of mathematical techniques all of which deserve a place in the armoury of the well-educated computer scientist. The objective is to present the ideas as a self-contained body of material, worthy of study in its own right, and at the same time to assist the learning of algebraic and coalgebraic methods, by ...
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Order-type Henstock and McShane integrals in banach lattice setting [PDF]
2014 IEEE 12th International Symposium on Intelligent Systems and Informatics (SISY), 2014 We study Henstock-type integrals for functions defined in a compact metric space $T$ endowed with a regular $σ$-additive measure $μ$, and taking values in a Banach lattice $X$. In particular, the space $[0,1]$ with the usual Lebesgue measure is considered.
CANDELORO, Domenico +1 more
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On modularity in lattices of congruences on ordered sets [PDF]
Czechoslovak Mathematical Journal, 1992 The author characterizes posets such that their lattices of congruences or convex congruences are modular or \(n\)-permutable.
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First Order Theories of Some Lattices of Open Sets
Logical Methods in Computer Science, 2017 We show that the first order theory of the lattice of open sets in some natural topological spaces is $m$-equivalent to second order arithmetic. We also show that for many natural computable metric spaces and computable domains the first order theory of the lattice of effectively open sets is undecidable. Moreover, for several important spaces (e.g., $\
Oleg Kudinov, Victor Selivanov
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The lattice of antichain cutsets of a partially ordered set
Discrete Mathematics, 1991 AbstractEvery finite lattice is isomorphic to the lattice of antichain cutsets of a finite partially ordered set whose chains have at most three elements.
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Atomic Boolean Lattice Completions of Ordered Sets
OrderAbstract We investigate posets that have an atomic Boolean lattice completion such that finite meets and joins are preserved by the embedding and the image of the poset under the embedding generates the Boolean lattice using complete lattice operations.
Wilmari Morton, Clint J. van Alten
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