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Permutations assigned to slim rectangular lattices

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Abstract

Slim rectangular lattices were introduced by G. Grätzer and E. Knapp in Acta Sci. Math. 75, 29–48, 2009. They are finite semimodular lattices L such that the poset Ji L of join-irreducible elements of L is the cardinal sum of two nontrivial chains. Using deep tools and involved considerations, a 2013 paper by G. Czédli and the present authors proved that a slim semimodular lattice is rectangular iff so is the Jordan–Hölder permutation associated with it. Here, we give an easier and more elementary proof.

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Authors and Affiliations

  1. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, Hungary, H-6720

    Tamás Dékány, Gergő Gyenizse & Júlia Kulin

Authors
  1. Tamás Dékány
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  2. Gergő Gyenizse
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  3. Júlia Kulin
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Corresponding author

Correspondence to Tamás Dékány.

Additional information

Communicated by G. Czédli

Research supported by the Hungarian National Foundation for Scientific Research grant no. K083219, K104251, and by the European Union, cofunded by the European Social Fund, under the project no. TÁMOP-4.2.2.A-11/1/KONV-2012-0073.

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Dékány, T., Gyenizse, G. & Kulin, J. Permutations assigned to slim rectangular lattices. ActaSci.Math. 82, 19–28 (2016). https://doi.org/10.14232/actasm-015-271-y

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  • DOI: https://doi.org/10.14232/actasm-015-271-y

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