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Simple Permutations with Order \(4n+2\) by Means of Pasting and Reversing

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Abstract

The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Humánez and Bernhardt (power of two). It is well known that Sharkovskii’s theorem shows the relationship between the cardinal of the set of periodic points of a continuous map, but simple permutations will show the behaviour of those periodic points. Recently Abdulla et al studied the structure of minimal \(4n+2\)-orbits of the continuous endomorphisms on the real line. This paper studies some combinatorial dynamics structures of permutations of mixed order \(4n+2\), describing its genealogy, using Pasting and Reversing.

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Authors and Affiliations

  1. Department of Mathematics, Universidad del Atlántico, KM 7 via Puerto Colombia, Barranquilla, Colombia

    Primitivo B. Acosta-Humánez

  2. INTELECTUAL.CO, Calle 2 No. 16B-134, Pradomar, Puerto Colombia

    Primitivo B. Acosta-Humánez

  3. School of Mathematics, Universidad Sergio Arboleda, Calle 74 No. 14-14, Bogotá, Colombia

    Óscar E. Martínez-Castiblanco

Authors
  1. Primitivo B. Acosta-Humánez
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  2. Óscar E. Martínez-Castiblanco
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Correspondence to Primitivo B. Acosta-Humánez.

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Dedicated to Jesús Hernando Pérez (Pelusa), teacher and friend.

The first author is partially supported by the MICIIN/FEDER Grant Number MTM2012-31714 Spanish Government, also by ECOS Nord France-Colombia No. C12M01 and Colciencias.

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Acosta-Humánez, P.B., Martínez-Castiblanco, Ó.E. Simple Permutations with Order \(4n+2\) by Means of Pasting and Reversing. Qual. Theory Dyn. Syst. 15, 181–210 (2016). https://doi.org/10.1007/s12346-015-0161-0

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  • DOI: https://doi.org/10.1007/s12346-015-0161-0

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