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DOI: 10.4230/LIPIcs.CPM.2021.11

Disorders and Permutations

Authors: Laurent Bulteau, Samuele Giraudo, and Stéphane Vialette

Published in: LIPIcs, Volume 191, 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)

Abstract

The additive x-disorder of a permutation is the sum of the absolute differences of all pairs of consecutive elements. We show that the additive x-disorder of a permutation of S(n), n ≥ 2, ranges from n-1 to ⌊n²/2⌋ - 1, and we give a complete characterization of permutations having extreme such values. Moreover, for any positive integers n and d such that n ≥ 2 and n-1 ≤ d ≤ ⌊n²/2⌋ - 1, we propose a linear-time algorithm to compute a permutation π ∈ S(n) with additive x-disorder d.

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Laurent Bulteau, Samuele Giraudo, and Stéphane Vialette. Disorders and Permutations. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{bulteau_et_al:LIPIcs.CPM.2021.11,
  author =	{Bulteau, Laurent and Giraudo, Samuele and Vialette, St\'{e}phane},
  title =	{{Disorders and Permutations}},
  booktitle =	{32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-186-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{191},
  editor =	{Gawrychowski, Pawe{\l} and Starikovskaya, Tatiana},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CPM.2021.11},
  URN =		{urn:nbn:de:0030-drops-139628},
  doi =		{10.4230/LIPIcs.CPM.2021.11},
  annote =	{Keywords: Permutation, Algorithm}
}

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Disorders and Permutations

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