Algebra universalis

, Volume 72, Issue 2, pp 155–162 | Cite as

Note on the description of join-distributive lattices by permutations



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.

Mathematics Subject Classification

Primary 06C10 secondary 05E99 

Key words and phrases

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


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Department of Mathematical SciencesYeshiva University, New YorkNew YorkUSA
  2. 2.Mathematics Department, School of Science and TechnologyNazarbayev UniversityAstanaRepublic of Kazakhstan
  3. 3.University of SzegedBolyai Institute. SzegedSzegedHungary

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