Gray Code for Permutations with a Fixed Number of Left-to-Right Minima

Abstract

In $[1]$, the author provided a Gray code for the set of $n$-length permutations with a given number of left-to-right minima in in-version array representation. In this paper, we give the first Gray code for the set of $n$-length permutations with a given number of left-to-right minima in one-line representation. In this code, each permutation is transformed into its successor by a product with a transposition or a cycle of length three. Also a generating algorithm for this code is given.