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Tight Multiple Twins in Permutations

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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Correspondence to Andrzej Dudek.

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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.

Communicated by Matjaz Konvalinka.

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

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