Lattice-inadmissible incidence structures
Frantisek Machala ; Vladimír Slezák
Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004), p. 199-209 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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 JLp 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 JLp.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:287747 
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1085,
     author = {Frantisek Machala and Vladim\'\i r Slez\'ak},
     title = {Lattice-inadmissible incidence structures},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {24},
     year = {2004},
     pages = {199-209},
     zbl = {1073.06004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1085}
}

Frantisek Machala; Vladimír Slezák. Lattice-inadmissible incidence structures. Discussiones Mathematicae - General Algebra and Applications, Tome 24 (2004) pp. 199-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1085/

[000] [1] P. Crawley and R.P. Dilworth, Algebraic Theory of Lattices, Prentice Hall, Englewood Cliffs 1973. | Zbl 0494.06001

[001] [2] G. Czédli, A.P. Huhn and E. T. Schmidt, Weakly independent sets in lattices, Algebra Universalis 20 (1985), 194-196. | Zbl 0569.06006

[002] [3] V. Dlab, Lattice formulation of general algebraic dependence, Czechoslovak Math. J. 20 (95) (1970), 603-615. | Zbl 0247.06006

[003] [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.

[004] [5] G. Gratzer, General Lattice Theory, Birkhauser-Verlag, Basel 1998. | Zbl 0909.06002

[005] [6] F. Machala, Join-independent and meet-independent sets in complete lattices, Order 18 (2001), 269-274. | Zbl 1009.06005

[006] [7] F. Machala, Incidence structures of independent sets, Acta Univ. Palacki. Olomuc., Fac. Rerum Natur., Math. 38 (1999), 113-118. | Zbl 0974.08001

[007] [8] F. Machala, Incidence structures of type (p,n), Czechoslovak Math. J. 53 (128) (2003), 9-18. | Zbl 1015.08001

[008] [9] F. Machala, Special incidence structures of type (p,n), Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Math. 39 (2000), 123-134. | Zbl 1040.08001

[009] [10] F. Machala, Special incidence structures of type (p,n) - Part II, Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Math. 40 (2001), 131-142.

[010] [11] V. Slezák, On the special context of independent sets, Discuss. Math. - Gen. Algebra Appl. 21 (2001), 115-122. | Zbl 0997.06003

[011] [12] G. Szász, Introduction to Lattice Theory, Akadémiai Kiadó, Budapest 1963.