Simple permutations with order $4n+2$ by means of Pasting and Reversing

Abstract

The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Humánez \& 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.

arXiv comment29 pages, 4 figures

References in corpus (3)

• On Pasting and Reversing operations over some rings
• Simple permutations with order $4n+2$. Part I
• Some Remarks on a Generalized Vector Product