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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 knownthat Sharkovskii's theorem shows the relationship between the cardinal of theset of periodic points of a continuous map, but simple permutations will showthe behaviour of those periodic points. Recently Abdulla et al studied thestructure of minimal $4n+2$-orbits of the continuous endomorphisms on the realline. This paper studies some combinatorial dynamics structures of permutationsof mixed order $4n+2$, describing its genealogy, using Pasting and Reversing.

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