Lattice-inadmissible incidence structures

Frantisek Machala; Vladimír Slezák

Discussiones Mathematicae - General Algebra and Applications (2004)

  • Volume: 24, Issue: 2, page 199-209
  • ISSN: 1509-9415

Abstract

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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 L p 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 L p .

How to cite

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Frantisek Machala, and Vladimír Slezák. "Lattice-inadmissible incidence structures." Discussiones Mathematicae - General Algebra and Applications 24.2 (2004): 199-209. <http://eudml.org/doc/287747>.

@article{FrantisekMachala2004,
abstract = {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 $J^\{p\}_\{L\}$.},
author = {Frantisek Machala, Vladimír Slezák},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {complete lattices; join-independent and meet-independent sets; incidence structures; complete lattice; join-independent set; meet-independent set; incidence structure},
language = {eng},
number = {2},
pages = {199-209},
title = {Lattice-inadmissible incidence structures},
url = {http://eudml.org/doc/287747},
volume = {24},
year = {2004},
}

TY - JOUR
AU - Frantisek Machala
AU - Vladimír Slezák
TI - Lattice-inadmissible incidence structures
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2004
VL - 24
IS - 2
SP - 199
EP - 209
AB - 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 $J^{p}_{L}$.
LA - eng
KW - complete lattices; join-independent and meet-independent sets; incidence structures; complete lattice; join-independent set; meet-independent set; incidence structure
UR - http://eudml.org/doc/287747
ER -

References

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  1. [1] P. Crawley and R.P. Dilworth, Algebraic Theory of Lattices, Prentice Hall, Englewood Cliffs 1973. Zbl0494.06001
  2. [2] G. Czédli, A.P. Huhn and E. T. Schmidt, Weakly independent sets in lattices, Algebra Universalis 20 (1985), 194-196. Zbl0569.06006
  3. [3] V. Dlab, Lattice formulation of general algebraic dependence, Czechoslovak Math. J. 20 (95) (1970), 603-615. Zbl0247.06006
  4. [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. [5] G. Gratzer, General Lattice Theory, Birkhauser-Verlag, Basel 1998. Zbl0909.06002
  6. [6] F. Machala, Join-independent and meet-independent sets in complete lattices, Order 18 (2001), 269-274. Zbl1009.06005
  7. [7] F. Machala, Incidence structures of independent sets, Acta Univ. Palacki. Olomuc., Fac. Rerum Natur., Math. 38 (1999), 113-118. Zbl0974.08001
  8. [8] F. Machala, Incidence structures of type (p,n), Czechoslovak Math. J. 53 (128) (2003), 9-18. Zbl1015.08001
  9. [9] F. Machala, Special incidence structures of type (p,n), Acta Univ. Palack. Olomuc., Fac. Rerum Natur., Math. 39 (2000), 123-134. Zbl1040.08001
  10. [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. [11] V. Slezák, On the special context of independent sets, Discuss. Math. - Gen. Algebra Appl. 21 (2001), 115-122. Zbl0997.06003
  12. [12] G. Szász, Introduction to Lattice Theory, Akadémiai Kiadó, Budapest 1963. 

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