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A note on blocks of skeleton tolerances

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Abstract

We provide a full characterization of lattices which can be blocks of the skeleton tolerance relation of a finite lattice. Moreover, we formulate a necessary condition for a lattice to be such a block in the case of finite distributive lattices with at most k-dimensional maximal boolean intervals.

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References

  1. H. J. Bandelt, Tolerance relations of lattices, Bull. Aust. Math. Soc., 23 (1981), 367–381.

    Article  MATH  MathSciNet  Google Scholar 

  2. I. Chajda, Algebraic Theory of Tolerance Relations, Univ. Palackého Olomouc (Olomouc, 1991).

    MATH  Google Scholar 

  3. G. Czédli, Factor lattices by tolerances, Acta Sci. Math. (Szeged), 44 (1982), 35–42.

    MATH  MathSciNet  Google Scholar 

  4. G. Czédli and G. Grätzer, Lattice tolerances and congruences, Algebra Universalis, 66 (2011), 5–6.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. Czédli, J. Grygiel and K. Grygiel, Distributive lattices determined by weighted double skeletons, Algebra Universalis, 69 (2013), 313–326.

    Article  MATH  MathSciNet  Google Scholar 

  6. G. Czédli and L. Klukovits, A note on tolerances of idempotent algebras, Glasnik Matematicki (Zagreb), 18 (1983), 35–38.

    Google Scholar 

  7. A. Day and Ch. Herrmann, Gluings of modular lattices, Order, 5 (1988), 85–101.

    Article  MATH  MathSciNet  Google Scholar 

  8. B. Ganter and R. Wille, Formal Concept Analysis: Mathematical Foundations, Springer-Verlag (Berlin, Heidelberg, New York, 1999).

    Book  MATH  Google Scholar 

  9. G. Grätzer and H. G. Wenzel, Notes on tolerance relations on lattices, Acta Sci. Math. (Szeged), 54 (1990), 229–240.

    MATH  MathSciNet  Google Scholar 

  10. J. Grygiel, The Concept of Gluing for Lattices, Wyższa Szkoła Pedagogiczna w Czȩstochowie (Czȩstochowa, 2004).

    Google Scholar 

  11. Ch. Herrmann, S-verklebte Summen von Verbänden, Math. Z., 130 (1973), 255–274.

    Article  MATH  MathSciNet  Google Scholar 

  12. D. Hobby and R. McKenzie, The Structure of Finite Algebras, AMS (Providence-Rhode Island, 1988).

    Book  Google Scholar 

  13. G. Markowsky, An overview of the poset of irreducibles, in: Combinatorial and Computational Mathematics: Present and Future, World Scientific (Singapore, 2001), pp. 162–177.

    Chapter  Google Scholar 

  14. K. Reuter, Counting formulas for glued lattices, Order, 1 (1985), 265–276.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Jan Długosz University in Czȩstochowa, Czȩstochowa, Poland

    Anetta Górnicka & Joanna Grygiel

  2. Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Prof. St. Łojasiewicza 6, 30-348, Kraków, Poland

    Katarzyna Grygiel

Authors
  1. Anetta Górnicka
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  2. Joanna Grygiel
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  3. Katarzyna Grygiel
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Corresponding author

Correspondence to Joanna Grygiel.

Additional information

This research was supported by the NSC of Poland, grant number 2011/01/B/HS1/00944. The third author worked on the paper while holding a post-doc position at the Jagiellonian University in Kraków within the SET project co-financed by the European Union.

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Górnicka, A., Grygiel, J. & Grygiel, K. A note on blocks of skeleton tolerances. Acta Math. Hungar. 143, 176–184 (2014). https://doi.org/10.1007/s10474-013-0375-z

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  • DOI: https://doi.org/10.1007/s10474-013-0375-z

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