Note on the description of join-distributive lattices by permutations

Let L be a join-distributive lattice with length n and width(Ji L ) ≤ 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 t...

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Bibliographic Details
Published inAlgebra universalis Vol. 72; no. 2; pp. 155 - 162
Main Authors Adaricheva, Kira, Czédli, Gábor
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.10.2014
Subjects
Algebra
Mathematics
Mathematics and Statistics
Primary 06C10
semimodular lattice
secondary 05E99
convex geometry
join-distributive lattice
trajectory
diamond-free lattice
permutation
antimatroid
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Summary:Let L be a join-distributive lattice with length n and width(Ji L ) ≤ 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.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-014-0295-y