Note on the description of join-distributive lattices by permutations

Kira Adaricheva, Gábor Czédli

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)155-162
    Number of pages8
    JournalAlgebra Universalis
    Volume72
    Issue number2
    DOIs
    Publication statusPublished - Oct 1 2014

    Fingerprint

    Distributive Lattice
    Join
    Permutation
    Trajectory

    Keywords

    • antimatroid
    • convex geometry
    • diamond-free lattice
    • join-distributive lattice
    • permutation
    • semimodular lattice
    • trajectory

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Note on the description of join-distributive lattices by permutations. / Adaricheva, Kira; Czédli, Gábor.

    In: Algebra Universalis, Vol. 72, No. 2, 01.10.2014, p. 155-162.

    Research output: Contribution to journalArticle

    Adaricheva, Kira ; Czédli, Gábor. / Note on the description of join-distributive lattices by permutations. In: Algebra Universalis. 2014 ; Vol. 72, No. 2. pp. 155-162.
    @article{c25fc22bcbd44b119c13deacb9117907,
    title = "Note on the description of join-distributive lattices by permutations",
    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.",
    keywords = "antimatroid, convex geometry, diamond-free lattice, join-distributive lattice, permutation, semimodular lattice, trajectory",
    author = "Kira Adaricheva and G{\'a}bor Cz{\'e}dli",
    year = "2014",
    month = "10",
    day = "1",
    doi = "10.1007/s00012-014-0295-y",
    language = "English",
    volume = "72",
    pages = "155--162",
    journal = "Algebra Universalis",
    issn = "0002-5240",
    publisher = "Birkhauser Verlag Basel",
    number = "2",

    }

    TY - JOUR

    T1 - Note on the description of join-distributive lattices by permutations

    AU - Adaricheva, Kira

    AU - Czédli, Gábor

    PY - 2014/10/1

    Y1 - 2014/10/1

    N2 - 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.

    AB - 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.

    KW - antimatroid

    KW - convex geometry

    KW - diamond-free lattice

    KW - join-distributive lattice

    KW - permutation

    KW - semimodular lattice

    KW - trajectory

    UR - http://www.scopus.com/inward/record.url?scp=84908129663&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=84908129663&partnerID=8YFLogxK

    U2 - 10.1007/s00012-014-0295-y

    DO - 10.1007/s00012-014-0295-y

    M3 - Article

    VL - 72

    SP - 155

    EP - 162

    JO - Algebra Universalis

    JF - Algebra Universalis

    SN - 0002-5240

    IS - 2

    ER -