[math-fun] Shuffling

Marc's comments made me think of the problem of shuffling. Suppose we don't want a random permutation, but rather want to "mix the input {0,1,2,...,n-1} as well as possible". In this sense: So that the average change in position over the numbers 0,...,n-1 is maximized. ------------------------------------------------------------ QUESTION: How can we make a list of permutations in order of most mixing to least mixing ??? QUESTION': Same question but with circular input Z/nZ (distance measured by shortest arc around the circle) ??? --Dan