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

Primitivo B. Acosta-Humánez ^[1] ; Óscar E. Martínez-Castiblanco ^[2]
1. [1] Universidad del Atlántico (Colombia)
  
  Universidad del Atlántico (Colombia)
  
  Colombia
2. [2] Universidad Sergio Arboleda
  
  Universidad Sergio Arboleda
  
  Colombia
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 15, Nº 1, 2016, págs. 181-210
Idioma: inglés
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Resumen
- 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.