2013/07/03 by Gábor Czédli, Czedli, Gabor
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Primary 06C10 #Rings and Algebras (math.RA) #Rough Sets and Fuzzy Logic #secondary 05A05 and 05B25 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1307.0900
openalex publication_date 2013/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, Czédli, 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.