Abstract
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, Czedli, 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.
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