Simple permutations with order $4n + 2$. Part I

Abstract

The problem of genealogy of permutations has been solved partially by Stefan (odd order) and Acosta-Hum\'anez & 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 behavior of those periodic points. This paper studies the structure of permutations of mixed order $4n+2$, its properties and a way to describe its genealogy by using Pasting and Reversing.