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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Published in | Algebra universalis Vol. 72; no. 2; pp. 155 - 162 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Basel
Springer Basel
01.10.2014
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Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0002-5240 1420-8911 |
DOI: | 10.1007/s00012-014-0295-y |