A subset X of a finite lattice L is CD-independent if the meet of any two
incomparable elements of X equals 0. In 2009, Cz\'edli, Hartmann and Schmidt
proved that any two maximal CD-independent subsets of a finite distributive
lattice have the same number of elements. In this paper, we prove that if L
is a finite meet-distributive lattice, then the size of every CD-independent
subset of L is at most the number of atoms of L plus the length of L. If,
in addition, there is no three-element antichain of meet-irreducible elements,
then we give a recursive description of maximal CD-independent subsets.
Finally, to give an application of CD-independent subsets, we give a new
approach to count islands on a rectangular board.Comment: 14 pages, 4 figure