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Note on the description of join-distributive lattices by permutations

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Abstract

Let L be a join-distributive lattice with length n and width(JiL) ≤ k. There are two ways to describe L by k − 1 permutations acting on an n-element set: a combinatorial way given by P.H. Edelman and R. E. Jamison in 1985 and a recent lattice theoretical way of the second author. We prove that these two approaches are equivalent. Also, we characterize join-distributive lattices by trajectories.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Yeshiva University, New York, 245 Lexington Ave., New York, NY, 10016, USA

    Kira Adaricheva

  2. Mathematics Department, School of Science and Technology, Nazarbayev University, 53 Kabanabay Batyr Ave., Astana, 010000, Republic of Kazakhstan

    Kira Adaricheva

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

    Gábor Czédli

Authors
  1. Kira Adaricheva
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  2. Gábor Czédli
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Correspondence to Gábor Czédli.

Additional information

Presented by J. Kung.

This research was supported by the NFSR of Hungary (OTKA), grant numbers K77432 and K83219, and by TÁMOP-4.2.1/B-09/1/KONV-2010-0005.

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Adaricheva, K., Czédli, G. Note on the description of join-distributive lattices by permutations. Algebra Univers. 72, 155–162 (2014). https://doi.org/10.1007/s00012-014-0295-y

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  • DOI: https://doi.org/10.1007/s00012-014-0295-y

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