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