On dedekind’s problem: The number of isotone boolean functions. II

Abstract

It is shown that ψ(n), the size of the free distributive lattice on n generators (which is the number of isotone Boolean functions on subsets of an n element set), satisfies (FORMAL PRESENTED)This result is an improvement by a factor √n in the 0 term of a previous result of Kleitman. In the course of deriving the main result, we analyze thoroughly the techniques used here and earlier by Kleitman, and show that the result in this paper is “best possible” (up to constant) using these techniques. © 1975 American Mathematical Society.