Gray Code of Generating Tree of n Permutation with m Cycles

Abstract

This paper proposes a new combinatorial Gray code. Combinatorial Gray code is a method of generating combinatorial objects so that every two successive objects differ as little as possible. Combinatorial object in this paper is a set of words that associated to Puspitodjati’s generating tree of n-length permutations with a given number of cycles. Nodes of the tree is labeled and then coded. The way nodes visited while traversing the tree constructs a new Gray code presented in this paper. The proof that it is a Gray code is given.