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Tight Multiple Twins in Permutations

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Abstract

Two permutations are similar if they have the same length and the same relative order. A collection of \(r\geqslant 2\) disjoint, similar subsequences of a permutation \(\pi \) forms r-twins in \(\pi \). We study the longest guaranteed length of r-twins which are tight in the sense that either each twin alone forms a block or their union does. We address the same question with respect to a random permutation.

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Acknowledgements

We would like to thank an anonymous referee for a careful reading of the manuscript and suggesting a number of editorial improvements.

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Authors and Affiliations

  1. Department of Mathematics, Western Michigan University, Kalamazoo, MI, USA

    Andrzej Dudek

  2. Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland

    Jarosław Grytczuk

  3. Department of Discrete Mathematics, Adam Mickiewicz University, Poznań, Poland

    Andrzej Ruciński

Authors
  1. Andrzej Dudek
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  2. Jarosław Grytczuk
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  3. Andrzej Ruciński
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Correspondence to Andrzej Dudek.

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Communicated by Matjaz Konvalinka.

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Andrzej Dudek was supported in part by Simons Foundation Grant #522400. Jarosław Grytczuk was supported in part by Narodowe Centrum Nauki, grant 2015/17/B/ST1/02660. Andrzej Ruciński was supported in part by Narodowe Centrum Nauki, grant 2018/29/B/ST1/00426.

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Dudek, A., Grytczuk, J. & Ruciński, A. Tight Multiple Twins in Permutations. Ann. Comb. 25, 1075–1094 (2021). https://doi.org/10.1007/s00026-021-00559-y

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