Notes on the description of join-distributive lattices by permutations

Abstract

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

8 pages, 1 figure

References in corpus (2)

• Coordinatization of join-distributive lattices
• Representing finite convex geometries by relatively convex sets

Cited by in corpus (5)

• A new property of congruence lattices of slim, planar, semimodular lattices
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• Slim patch lattices as absolute retracts and maximal lattices
• Length-preserving extensions of semimodular lattices by lowering join-irreducible elements
• Lattices with many congruences are planar