Lesson 7

It is not difficult to write explicit formulas for \(|B_{n} \cap \mathcal{S}_{0}|\) (i.e., the number of functions of \(n\) variables that preserve zero), \(|B_{n} \cap \mathcal{L}|\) (linear functions), and \(|B_{n} \cap \mathcal{D}|\) (self-dual functions). But with monotone functions, things are more complicated. The number \(M(n)=|B_{n} \cap \mathcal{M}|\) is called the Dedekind number. In 2023, it was found that \[M(9)=286386577668298411128469151667598498812366\ .\]