On the length of the lattice of sublattices of a finite distributive lattice (Q5894757)

Let \(L\) be a finite distributive lattice and let \(\text{Sub}(L)\) be the lattice of all sublattices of \(L\). Next let \(l(\text{Sub}(L))\) be the length of \(\text{Sub}(L)\). A formula for \(l(\text{Sub}(L))\) was found by \textit{K. M. Koh} [ibid. 16, 282-286 (1983; Zbl 0528.06013)]. In the paper under review a new formula for \(l(\text{Sub}(L))\) is proved which is expressed in terms of formal concept analysis. As a consequence, the author shows that if \(L\) is the free distributive lattice on \(n\) generators, then \(l(\text{Sub}(L))= 2^{2n-1}+ 3.2^{n-1}- 3^ n-1\).