Let $\mathcal{L}$ be a finite distributive lattice, then it is known that it can be embedded into a finite boolean lattice (see theorem 8.5. p91 in [this note](http://www.math.hawaii.edu/~jb/math618/os8uh.pdf)). 


Let $n$ be the length of $\mathcal{L}$ and let $\mathcal{B}\_n$ be the boolean lattice of rank $n$.


*Question*: Can $\mathcal{L}$ be embedded into $\mathcal{B}\_n$?



Can a length n distributive lattice be embedded into Bn?
A distributive lattice $L$ of length $n$ is isomorphic to the set of order ideals of an $n$-element poset $P$, ordered by inclusion. This is the Fundamental Theorem of Finite Distributive Lattices, first proved by Garrett Birkhoff. Thus $L$ imbeds into the boolean algebra of all subsets of $P$.


