Loopless generation of Gray codes for k-ary trees

Abstract

A number of loopless binary and k-ary tree generation algorithms are known. Vajnovszki recently presented a loopless Gray code generation algorithm for binary trees based on rotations and variations. He used a representation introduced by Pallo and generated the Gray code of Roelants van Baronaigien and Ruskey. In this paper we generalize the representation to k-ary trees and base the loopless generation algorithm on the shifts of Korsh and Lipschutz.