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**A lemma and a conjecture on the cost of rearrangements.**
*(English)*
Zbl 1114.05002

Given a line of books, which are either of black cover or of white cover, what is the minimum cost of sorting them out using transpositions (of blocks) so that books of the same color are put one after another? The lemma referred to in the title is the main result of this paper and states that the cost is at least logarithmic under certain assumptions on the configuration of books. Two (not one but closely related) conjectures are formulated for a continuous version of the problem.

Reviewer: Hsien-Kuei Hwang (Taipei)

### MSC:

05A05 | Permutations, words, matrices |

35L65 | Hyperbolic conservation laws |

35Q35 | PDEs in connection with fluid mechanics |

35R25 | Ill-posed problems for PDEs |

37C60 | Nonautonomous smooth dynamical systems |

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\textit{A. Bressan}, Rend. Semin. Mat. Univ. Padova 110, 97--102 (2003; Zbl 1114.05002)

### References:

[1] | A. BRESSAN, An ill posed Cauchy problem for a hyperbolic system in two space dimensions, Rend. Sem. Mat. Univ. Padova, in this volume p. 103. Zbl1114.35123 MR2033003 · Zbl 1114.35123 |

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