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Distributive lattices determined by weighted double skeletons

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Abstract

Related to his S-glued sum construction, the skeleton S(L) of a finite lattice L was introduced by C. Herrmann in 1973. Our theorem asserts that if D is a finite distributive lattice and its second skeleton, S(S(D)), is the trivial lattice, then D is characterized by its weighted double skeleton, introduced by the second author in 2006. The assumption on the second skeleton is essential.

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Authors and Affiliations

  1. University of Szeged, Szeged, 6720, HUNGARY

    Gábor Czédli

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

    Joanna Grygiel

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

    Katarzyna Grygiel

Authors
  1. Gábor Czédli
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  2. Joanna Grygiel
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  3. Katarzyna Grygiel
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Corresponding author

Correspondence to Gábor Czédli.

Additional information

Presented by M. Ploscica.

This research of the first author was supported by the NFSR of Hungary (OTKA), grant numbers K77432 and K83219. The second author was supported by the NSC of Poland, grant number 2011/01/B/HS1/00944. The third author was supported by the NSC of Poland, grant number 2011/01/B/HS1/00944, and by the Polish Ministry of Science and Higher Education, grant number NN206 376137.

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Czédli, G., Grygiel, J. & Grygiel, K. Distributive lattices determined by weighted double skeletons. Algebra Univers. 69, 313–326 (2013). https://doi.org/10.1007/s00012-013-0232-5

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  • DOI: https://doi.org/10.1007/s00012-013-0232-5

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