Gray Code for Cayley Permutations

A length-n Cayley permutation p of a total ordered set S is a length-n sequence of elements from S, subject to the condition that if an element x appears in p then all elements y < x also appear in p. In this paper, we give a Gray code list for the set of length-n Cayley permutations. Two successive permutations in this list differ at most in two positions