  Join-distributive lattices are finite, meet-semidistributive, and semimodular
lattices. They are the same as Dilworth's lattices in 1940, and many
alternative definitions and equivalent concepts have been discovered or
rediscovered since then. Let L be a join-distributive lattice of length n and
let k denote the width of the set of join-irreducible elements of L. A result
of P.H. Edelman and R.E. Jamison, translated from Combinatorics to Lattice
Theory, says that L can be described by k-1 permutations acting on the set
{1,...,n}. We prove a similar result within Lattice Theory: there exist k-1
permutations acting on {1,...,n} such that the elements of L are coordinatized
by k-tuples over {0,...,n}, and the permutations determine which k-tuples are
allowed. Since the concept of join-distributive lattices is equivalent to that
of antimatroids and convex geometries, our result offers a coordinatization for
these combinatorial structures.
