A Lemma and a Conjecture on the Cost of Rearrangements

Details A Lemma and a Conjecture on the Cost of Rearrangements A Lemma and a Conjecture on the Cost of Rearrangements

2003-02-19

arxiv.org/abs/math/0302228v1

Mathematics

Analysis of PDEs

2 figures, 4 pages

Scientific paper

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.

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