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 in:Algebra universalis 2014-10, Vol.72 (2), p.155-162
Main Authors: Adaricheva, Kira, Czédli, Gábor
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
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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