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Browsing Articles by Author "Adaricheva, Kira"

Browsing Articles by Author "Adaricheva, Kira"

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  • A class of infinite convex geometries 
    Adaricheva, Kira; Nation, J.B. (2015)
    Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower ...
  • Algebraic convex geometries revisited 
    Adaricheva, Kira (2014)
    Representation of convex geometry as an appropriate join of compatible orderings of the base set can be achieved, when closure operator of convex geometry is algebraic, or finitary. This bears to the finite case proved by ...
  • Discovery of the D-basis in binary tables based on hypergraph dualization 
    Adaricheva, Kira; Nation, J.B. (2016)
    Discovery of (strong) association rules, or implications, is an important task in data management, and it nds application in arti cial intelligence, data mining and the semantic web. We introduce a novel approach for ...
  • Embedding finite lattices into finite biatomic lattices 
    Adaricheva, Kira; Wehrung, Freidrich (2005)
    For a class C of finite lattices, the question arises whether any lattice in C can be embedded into some atomistic, biatomic lattice in C. We provide answers to the question above for C being, respectively, — The class ...
  • Join-semidistributive lattices of relatively convex sets 
    Adaricheva, Kira (2004)
    We give two sufficient conditions for the lattice Co(Rn,X) of rel- atively convex sets of Rn to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice can ...
  • Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part I 
    Adaricheva, Kira; Nation, J. B. (2012)
    We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice ...
  • Lattices of quasi-equational theories as congruence lattices of semilattices with operators, part II 
    Adaricheva, Kira; Nation, J.B. (2012)
    Part I proved that for every quasivariety K of structures (which may have both operations and relations) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the ...
  • Notes on the description of join-distributive lattices by permutations 
    Adaricheva, Kira; Cz´edli, G´abor (2012)
    Let L be a join-distributive lattice with length n and width (Ji L) k. There are two ways to describe L by k − 1 permutations acting on an n-element set: a combinatorial way given by P.H. Edelman and R. E. Jamison in ...
  • On complex algebras of subalgebras 
    Adaricheva, Kira; Pilitowska, Agata; Stanovsky, David (2006)
    Let V be a variety of algebras. We establish a condition (so called generalized entropic property), equivalent to the fact that for every algebra A 2 V, the set of all subalgebras of A is a subuniverse of the complex ...
  • On implicational bases of closure system with unique critical sets 
    Adaricheva, Kira; Nation, J.B. (2013)
    We show that every optimum basis of a nite closure system, in D. Maier's sense, is also right-side optimum, which is a parameter of a minimum CNF representation of a Horn Boolean function. New parameters for the size ...
  • On scattered convex geometries 
    Adaricheva, Kira; Pouzet, Maurice (2015)
    A convex geometry is a closure space satisfying the anti-exchange axiom. For several types of algebraic convex geometries we describe when the collection of closed sets is order scattered, in terms of obstructions to the ...
  • Optimum basis of finite convex geometry 
    Adaricheva, Kira (2016)
    Convex geometries form a subclass of closure systems with unique criticals, or UC-systems. We show that the F-basis introduced in [6] for UC- systems, becomes optimum in convex geometries, in two essential parts of ...
  • Ordered direct implication basis of a finite closure system 
    Adaricheva, Kira; Nation, J.B.; Rand, R. (2012)
    Closure system on a nite set is a unifying concept in logic programming, relational data bases and knowledge systems. It can also be presented in the terms of nite lattices, and the tools of economic description of a ...
  • Realization of abstract convex geometries by point configurations. Part I 
    Adaricheva, Kira; Wild, Marcel (2007)
    The Edelman-Jamison problem is to characterize those abstract convex geometries that are representable by a set of points in the plane. We show that some natural modification of the Edelman-Jamison problem is equivalent to ...
  • Representing finite convex geometries by relatively convex sets 
    Adaricheva, Kira (2011)
    A closure system with the anti-exchange axiom is called a convex geometry. One geometry is called a sub-geometry of the other if its closed sets form a sublattice in the lattice of closed sets of the other. We prove that ...
  • Stasheff polytope as a sublattice of permutohedron 
    Adaricheva, Kira (2011)
    An assosiahedron Kn, known also as Stasheff polytope, is a multifaceted combinatorial object, which, in particular, can be realized as a convex hull of certain points in Rn, forming (n − 1)-dimensional polytope1. A ...