Classification of permutations and cycles of maximum topological entropy

Iff is a continuous self-map of a compact interval we can represent each finite fully invariant set off by a permutation. We can then calculate the topological entropy of the permutation. This provides us with a numerical measure of complexity for any map which exhibits a given permutation type. In this paper we present cyclic and noncyclic permutations which have maximum topological entropy amongst all cyclic or noncyclic permutations of the same length.