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Volumn 6, Issue 2, 2004, Pages 163-190

Some lattices of closure systems on a finite set

Author keywords

(Locally distributive) lattice; Anti exchange closure operator; Closure system; Convex geometry; Quasi closed set

Indexed keywords


EID: 15044347296     PISSN: 13658050     EISSN: 13658050     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (15)

References (40)
  • 1
    • 0030459331 scopus 로고    scopus 로고
    • Maximal sublattices of finite distributive lattices
    • M. E. Adams, P. Dwinger and J. Schmid, Maximal sublattices of finite distributive lattices, Algebra Universalis 36, 488-504, 1996.
    • (1996) Algebra Universalis , vol.36 , pp. 488-504
    • Adams, M.E.1    Dwinger, P.2    Schmid, J.3
  • 2
    • 34250296845 scopus 로고
    • Chaînes maximales de préordres
    • J. C. Arditti and R. Cori, Chaînes maximales de préordres, Aequationes Math. 15(1), 49-54, 1977.
    • (1977) Aequationes Math. , vol.15 , Issue.1 , pp. 49-54
    • Arditti, J.C.1    Cori, R.2
  • 3
    • 0001454571 scopus 로고
    • Dependency structures of data base relationships
    • North Holland, Amsterdam
    • W. W. Armstrong, Dependency structures of data base relationships, Information Processing 74, 580-583, North Holland, Amsterdam, 1974.
    • (1974) Information Processing , vol.74 , pp. 580-583
    • Armstrong, W.W.1
  • 5
    • 0004190631 scopus 로고
    • American Mathematical Society, Providence, 1967, 3rd ed.
    • G. Birkhoff, Lattice Theory, American Mathematical Society, Providence, 1940 (1967, 3rd ed.).
    • (1940) Lattice Theory
    • Birkhoff, G.1
  • 6
    • 21744454250 scopus 로고    scopus 로고
    • Reducible classes of finite lattices
    • G. H. Bordalo and B. Monjardet, Reducible classes of finite lattices, Order 13 (4), 379-390, 1996.
    • (1996) Order , vol.13 , Issue.4 , pp. 379-390
    • Bordalo, G.H.1    Monjardet, B.2
  • 7
    • 0036433198 scopus 로고    scopus 로고
    • The lattice of strict completions of a finite poset
    • G. H. Bordalo and B. Monjardet, The lattice of strict completions of a finite poset, Algebra Universalis 47, 183-200, 2002.
    • (2002) Algebra Universalis , vol.47 , pp. 183-200
    • Bordalo, G.H.1    Monjardet, B.2
  • 8
    • 0042614624 scopus 로고
    • The poset of closures as model of changing databases
    • G. Burosch, J. Demetrovics and G. Katona, The poset of closures as model of changing databases, Order 4, 30-59, 1987.
    • (1987) Order , vol.4 , pp. 30-59
    • Burosch, G.1    Demetrovics, J.2    Katona, G.3
  • 9
    • 0037447220 scopus 로고    scopus 로고
    • The lattices of closure systems, closure operators and implicational systems on a finite set: A survey
    • N. Caspard and B. Monjardet, The lattices of closure systems, closure operators and implicational systems on a finite set: a survey, Discrete Applied Mathematics, 127 (2), 241-269, 2003.
    • (2003) Discrete Applied Mathematics , vol.127 , Issue.2 , pp. 241-269
    • Caspard, N.1    Monjardet, B.2
  • 10
    • 0011359466 scopus 로고
    • Frattini sublattices of distributive lattices
    • C. C. Chen, K. M. Koh and S. K. Tan, Frattini sublattices of distributive lattices, Algebra Universalis 3 (3), 294-303, 1973.
    • (1973) Algebra Universalis , vol.3 , Issue.3 , pp. 294-303
    • Chen, C.C.1    Koh, K.M.2    Tan, S.K.3
  • 13
    • 0003094802 scopus 로고
    • Characterization of finite lattices that are bounded-homomorphic images or sublattices of free lattices
    • A. Day, Characterization of finite lattices that are bounded-homomorphic images or sublattices of free lattices, Canad. J. Math. 31, 69-78, 1979.
    • (1979) Canad. J. Math. , vol.31 , pp. 69-78
    • Day, A.1
  • 14
    • 38249007910 scopus 로고
    • Functional dependencies in relational databases: A lattice point of view
    • J. Demetrovics, L. O. Libkin and I. B. Muchnik, Functional dependencies in relational databases: a lattice point of view, Discrete Applied Mathematics 40, 155-185, 1992.
    • (1992) Discrete Applied Mathematics , vol.40 , pp. 155-185
    • Demetrovics, J.1    Libkin, L.O.2    Muchnik, I.B.3
  • 16
    • 0042189103 scopus 로고
    • Abstract convexity and meet-distributive lattices
    • P. H. Edelman, Abstract convexity and meet-distributive lattices, Contemporary Mathematics 57, 127-150, 1986.
    • (1986) Contemporary Mathematics , vol.57 , pp. 127-150
    • Edelman, P.H.1
  • 17
    • 0006862537 scopus 로고
    • Combinatorial representations and convex dimension of convex geometries
    • P. H. Edelman and M. E. Saks, Combinatorial representations and convex dimension of convex geometries, Order 5 (1), 23-32, 1988.
    • (1988) Order , vol.5 , Issue.1 , pp. 23-32
    • Edelman, P.H.1    Saks, M.E.2
  • 18
    • 21344448799 scopus 로고
    • Intervals in Lattices of Quasiorders
    • M. Erné and J. Rheinold, Intervals in Lattices of Quasiorders, Order 12, 375-403, 1995.
    • (1995) Order , vol.12 , pp. 375-403
    • Erné, M.1    Rheinold, J.2
  • 21
    • 0012150507 scopus 로고
    • Algorithmen zur formalen Begriffsanalyse
    • published (B. Ganter, R. Wille and K.E. Wolff, eds), Wissenchaftverlag, Mannheim
    • published as Algorithmen zur formalen Begriffsanalyse, in Beitraege zur Begriffsanalyse, (B. Ganter, R. Wille and K.E. Wolff, eds), Wissenchaftverlag, Mannheim (1987) 241-254.
    • (1987) Beitraege zur Begriffsanalyse , pp. 241-254
  • 22
  • 23
    • 0002819235 scopus 로고
    • Families minimales d'implications informatives résultant d'un tableau de données binaires
    • L. Guigues and V. Duquenne, Families minimales d'implications informatives résultant d'un tableau de données binaires, Mathématiques et Sciences humaines 95, 5-18, 1986.
    • (1986) Mathématiques et Sciences Humaines , vol.95 , pp. 5-18
    • Guigues, L.1    Duquenne, V.2
  • 26
    • 0013032470 scopus 로고    scopus 로고
    • Choice functions and abstract convex geometries
    • G. A. Koshevoy, Choice functions and abstract convex geometries, Mathematical Social Sciences 38 (1), 35-44, 1999.
    • (1999) Mathematical Social Sciences , vol.38 , Issue.1 , pp. 35-44
    • Koshevoy, G.A.1
  • 28
    • 10044238680 scopus 로고
    • Latticial Theory of Consensus
    • V. Barnett, H. Moulin, M. Salles and N. Schofiels, eds, Cambridge University Press
    • B. Leclerc and B. Monjardet, Latticial Theory of Consensus, in Social Science, Welfare and Ethics, V. Barnett, H. Moulin, M. Salles and N. Schofiels, eds, Cambridge University Press, 145-160, 1995.
    • (1995) Social Science, Welfare and Ethics , pp. 145-160
    • Leclerc, B.1    Monjardet, B.2
  • 29
    • 56249146222 scopus 로고
    • Treillis d'ordres
    • work for the seminary of Aix-en-Provence on the orders, Gauthier-Villars, Paris
    • B. Monjardet, Treillis d'ordres, in Ordres, work for the seminary of Aix-en-Provence on the orders, Gauthier-Villars, Paris, 29-45, 1971.
    • (1971) Ordres , pp. 29-45
    • Monjardet, B.1
  • 30
    • 0002815916 scopus 로고
    • The consequences of Dilworth's work on lattices with unique irreducible decompositions
    • K.P. Bogart, R. Freese and J. Kung, (Eds), Birkhäuser, Boston
    • B. Monjardet, The consequences of Dilworth's work on lattices with unique irreducible decompositions. In: K.P. Bogart, R. Freese and J. Kung, (Eds), The Dilworth theorems Selected papers of Robert P. Dilworth. Birkhäuser, Boston, 192-201, 1990.
    • (1990) The Dilworth Theorems Selected Papers of Robert P. Dilworth , pp. 192-201
    • Monjardet, B.1
  • 31
    • 38249020058 scopus 로고
    • Arrowian characterizations of latticial federation consensus functions
    • B. Monjardet, Arrowian characterizations of latticial federation consensus functions, Mathematical Social Sciences 20 (1), 51-71, 1990.
    • (1990) Mathematical Social Sciences , vol.20 , Issue.1 , pp. 51-71
    • Monjardet, B.1
  • 32
    • 0043133505 scopus 로고    scopus 로고
    • On a dependance relation in finite lattices
    • B. Monjardet and N. Caspard, On a dependance relation in finite lattices, Discrete Mathematics 165/166, 497-505, 1997.
    • (1997) Discrete Mathematics , vol.165-166 , pp. 497-505
    • Monjardet, B.1    Caspard, N.2
  • 33
    • 0042905591 scopus 로고    scopus 로고
    • The duality between the anti-exchange closure operators and the path independent choice operators on a finite set
    • B. Monjardet and V. Raderanirina, The duality between the anti-exchange closure operators and the path independent choice operators on a finite set, Mathematical Social Sciences 41 (2), 131-150, 2001.
    • (2001) Mathematical Social Sciences , vol.41 , Issue.2 , pp. 131-150
    • Monjardet, B.1    Raderanirina, V.2
  • 35
    • 84939503255 scopus 로고
    • Some studies on closure relations
    • O. re, Some studies on closure relations, Duke Mathematical Journal 10, 761-785, 1983.
    • (1983) Duke Mathematical Journal , vol.10 , pp. 761-785
    • Re, O.1
  • 36
    • 84966224063 scopus 로고
    • Maximal sublattices of finite distributive lattices
    • I. Rival, Maximal sublattices of finite distributive lattices, Proc. Amer. Math. Soc. 37, 417-420, 1973.
    • (1973) Proc. Amer. Math. Soc. , vol.37 , pp. 417-420
    • Rival, I.1
  • 37
    • 84968487243 scopus 로고
    • Maximal sublattices of finite distributive lattices II
    • I. Rival, Maximal sublattices of finite distributive lattices II, Proc. Amer. Math. Soc. 44, 263-268, 1974.
    • (1974) Proc. Amer. Math. Soc. , vol.44 , pp. 263-268
    • Rival, I.1
  • 38
    • 0141576873 scopus 로고    scopus 로고
    • Quasiorders and sublattices of distributive lattices
    • J. Schmid, Quasiorders and sublattices of distributive lattices, Order 19, 11-34, 2002.
    • (2002) Order , vol.19 , pp. 11-34
    • Schmid, J.1
  • 39
    • 0012875487 scopus 로고    scopus 로고
    • Semimodular lattices
    • Cambridge University Press, Cambridge
    • M. Stern, Semimodular lattices, Encyclopedia of Mathematics, Cambridge University Press, Cambridge, 1999.
    • (1999) Encyclopedia of Mathematics
    • Stern, M.1
  • 40
    • 0011603823 scopus 로고
    • A theory of finite closure spaces based on implications
    • M. Wild, A theory of finite closure spaces based on implications, Advances in Mathematics 108 (1) 118-139, 1994.
    • (1994) Advances in Mathematics , vol.108 , Issue.1 , pp. 118-139
    • Wild, M.1


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