CD-independent subsets in meet-distributive lattices.
For the notion of CD-independent subset in a distributive lattice, see \textit{G. Czédli, M. Hartmann, E. T. Schmidt} [Publ. Math. 74, No. 1-2, 127-134 (2009; Zbl 1199.06032)]. (These subsets are known also as laminar systems; see, e.g., \textit{P. P. Pach, G. Pluhár, A. Pongrácz, Cs. Szabó} [J. Math. Anal. Appl. 375, No. 1, 8-13 (2011; Zbl 1291.05020)].) In the paper under review, the main result of \textit{G. Czédli} et al. [loc. cit.] is generalised to meet-distributive lattices: it is proved that the size of a maximal CD-independent subset in a finite meet-distributive lattice does not exceed the number of atoms of the lattice plus its length. Some additional information on such subsets is obtained for several special subclasses of finite meet-distributive lattices. Another connection with the mentioned previous paper is through an application of CD-independent subsets: a new approach to counting islands on a rectangular board is developed.
scientific article; zbMATH DE number 6330508
scientific article