Geodesic
Lattice-inadmissible incidence structures
Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 199-209.

Voir la notice de l'article provenant de la source Library of Science

Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure J^p_L of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure J^p_L.
Keywords: complete lattices, join-independent and meet-independent sets, incidence structures 
@article{DMGAA_2004_24_2_a3,
     author = {Machala, Frantisek and Slez\'ak, Vladim{\'\i}r},
     title = {Lattice-inadmissible incidence structures},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {199--209},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2004_24_2_a3/}
}
TY  - JOUR
AU  - Machala, Frantisek
AU  - Slezák, Vladimír
TI  - Lattice-inadmissible incidence structures
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2004
SP  - 199
EP  - 209
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2004_24_2_a3/
LA  - en
ID  - DMGAA_2004_24_2_a3
ER  - 
%0 Journal Article
%A Machala, Frantisek
%A Slezák, Vladimír
%T Lattice-inadmissible incidence structures
%J Discussiones Mathematicae. General Algebra and Applications
%D 2004
%P 199-209
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2004_24_2_a3/
%G en
%F DMGAA_2004_24_2_a3
Machala, Frantisek; Slezák, Vladimír. Lattice-inadmissible incidence structures. Discussiones Mathematicae. General Algebra and Applications, Tome 24 (2004) no. 2, pp. 199-209. http://geodesic.mathdoc.fr/item/DMGAA_2004_24_2_a3/

[1] P. Crawley and R.P. Dilworth, Algebraic Theory of Lattices, Prentice Hall, Englewood Cliffs 1973.

[2] G. Czédli, A.P. Huhn and E. T. Schmidt, Weakly independent sets in lattices, Algebra Universalis 20 (1985), 194-196.

[3] V. Dlab, Lattice formulation of general algebraic dependence, Czechoslovak Math. J. 20 (95) (1970), 603-615.

[4] B. Ganter and R. Wille, Formale Begriffsanalyse. Mathematische Grundlagen, Springer-Verlag, Berlin 1996; Eglish translation: Formal Concept Analysis. Mathematical Fundations, Springer-Verlag, Berlin 1999.

[5] G. Gratzer, General Lattice Theory, Birkhauser-Verlag, Basel 1998.

[6] F. Machala, Join-independent and meet-independent sets in complete lattices, Order 18 (2001), 269-274.

[7] F. Machala, Incidence structures of independent sets, Acta Univ. Palacki. Olomuc., Fac. Rerum Natur., Math. 38 (1999), 113-118.

[8] F. Machala, Incidence structures of type (p,n), Czechoslovak Math. J. 53 (128) (2003), 9-18.

[9] F. Machala, Special incidence structures of type (p,n), Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Math. 39 (2000), 123-134.

[10] F. Machala, Special incidence structures of type (p,n) - Part II, Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Math. 40 (2001), 131-142.

[11] V. Slezák, On the special context of independent sets, Discuss. Math. - Gen. Algebra Appl. 21 (2001), 115-122.

[12] G. Szász, Introduction to Lattice Theory, Akadémiai Kiadó, Budapest 1963.