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  • 1
    Electronic Resource
    Electronic Resource
    On context patterns associated with concept lattices (1993)
    Springer
    Order 10 (1993), S. 363-373 
    Details
    ISSN: 1572-9273
    Keywords: 06B05 ; 06A15 ; Context ; arrow relation ; concept lattice ; context pattern ; strictly realizable context pattern
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the following reconstruction problem: Given two ordered sets (G, ≤) and (M, ≤) representing join- and meet-irreducible elements, respectively together with three relationsJ, , $${\hbox{\ \hbox{$\mid$}\kern -1em\lower .5em \hbox{$\leftarrow$}}} $$ onG×M modelling comparability (g≤m) and maximal noncomparability with respect tog (g≰m, butg≤m*) and with respect tom (g≰m, butg≤m*). We determine necessary and sufficient conditions for the existence of a finite latticeL and injections α:G→J(L) and β:M→M(L) such that the given order relations and the abstract relations coincide with the one induced by the latticeL.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01108830
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Generalizing semidistributivity (1993)
    Springer
    Order 10 (1993), S. 77-92 
    Details
    ISSN: 1572-9273
    Keywords: 06B05 ; 06B20 ; Doubling construction ; semidistributive lattices ; k-semidistributivity ; context ; doubling classes ; pseudovariety
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A latticeL is called congruence normal if it can be generated by doubling of convex sets starting with the one-element lattice. In the special case of intervals, the lattice is called bounded. It has been proven thatL is bounded if and only ifL is congruence normal and semidistributive. In this paper we study the connection between certain classes of convex sets and generalized semidistributive laws. These so-called doubling classes are pseudovarieties which can be described by implications as well as by forbiden substructures. In the end, we examine the structure of the lattice of all doubling classes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01108710
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    Paper (German National Licenses)
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  • 3
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    On Tamari lattices (1994)
    Elsevier
    Details
    Publication Date: 1994-10-01
    Print ISSN: 0012-365X
    Electronic ISSN: 1872-681X
    Topics: Mathematics
    Published by Elsevier
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