More restricted growth functions: Gray codes and exhaustive generations

TL;DR

This paper explores Gray codes for restricted growth functions, introducing new variations and providing the first efficient algorithms for generating bounded restricted growth functions.

Contribution

It introduces new variations of Gray code orderings and presents the first efficient algorithms for generating bounded restricted growth functions.

Findings

Developed new Gray code variations for restricted growth functions.

Provided the first efficient algorithms for bounded restricted growth functions.

Extended previous work on Gray codes for combinatorial objects.

Abstract

A Gray code for a combinatorial class is a method for listing the objects in the class so that successive objects differ in some prespecified, small way, typically expressed as a bounded Hamming distance. In a previous work, the authors of the present paper showed, among other things, that the $m$-ary Reflected Gray Code Order yields a Gray code for the set of restricted growth functions. Here we further investigate variations of this order relation, and give the first Gray codes and efficient generating algorithms for bounded restricted growth functions.