Abstract

ACOSTA HUMANEZ, PRIMITIVO B.. Genealogy of simple permutations with order a power of two. Rev.colomb.mat. [online]. 2008, vol.42, n.1, pp.1-14. ISSN 0034-7426.

The aim of this paper is to show some properties of simple permutations with order a power of two and to give a combinatorial formula to determine its genealogy involving two new operations: the pasting operation and reversing. Simple permutations are very important because corresponds to primary orbits or minimal orbits and in particular, simple permutations with order a power of two are related with the right side in the Sharkovskiis order.

Keywords : Bernhardt's theorem; Markov's graphs; partial ordering ofpermutations; reversing operation; pasting operation; Sharkovskii's theorem; simple orbits ofBlock.

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