MAXIMAL ENTROPY OF PERMUTATIONS OF EVEN ORDER

A finite invariant set of a continuous map of an interval induces a pe rmutation called its type. If this permutation is a cycle, it is calle d its orbit type. It has been shown by Geller and Tolosa that Misiurew icz-Nitecki orbit types of period n congruent to 1 (mod 4) and their g eneralizations to orbit types of period n congruent to 3 (mod 4) have maximal entropy among all orbit types of odd period n, and indeed amon g all permutations of period n. We further generalize this family to p ermutations of even period n and show that they again attain maximal e ntropy amongst n-permutations.