  Consider a stack of books, containing both white and black books. Suppose
that we want to sort them out, putting the white books on the right, and the
black books on the left (fig.~1). This will be done by a finite sequence of
elementary transpositions. In other words, if we have a stack of all black
books of length $a$ followed by a stack of all white books of length $b$, we
are allowed to reverse their order at the cost of $a+b$. We are interested in a
lower bound on the total cost of the rearrangement.
