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

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