License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2021.11
URN: urn:nbn:de:0030-drops-139628
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Bulteau, Laurent ; Giraudo, Samuele ; Vialette, Stéphane

Disorders and Permutations

LIPIcs-CPM-2021-11.pdf (1 MB)


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.

BibTeX - Entry

  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 =		{},
  URN =		{urn:nbn:de:0030-drops-139628},
  doi =		{10.4230/LIPIcs.CPM.2021.11},
  annote =	{Keywords: Permutation, Algorithm}

Keywords: Permutation, Algorithm
Collection: 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021)
Issue Date: 2021
Date of publication: 30.06.2021

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