Why Concept Lattices Are Large - Extremal Theory for the Number of Minimal Generators and Formal Concepts.
Alexandre Albano, Bogdan Chornomaz · Concept Lattices and their Applications · 2015
A unique type of subcontexts is always present in formal contexts with many concepts: the contranominal scales. We make this precise by giving an upper bound for the number of minimal generators (and thereby for the number of concepts) of contexts without contranominal scales larger than a given size. Extremal contexts are constructed which meet this bound exactly. They are completely classified.