Two Reflected Gray Code based orders on some restricted growth sequences

TL;DR

This paper introduces two Gray code-based orderings applied to restricted growth sequences, providing efficient algorithms for generation and demonstrating their effectiveness across various sequence sets.

Contribution

It presents two new order relations based on reflected Gray codes for restricted growth sequences and offers efficient algorithms for their exhaustive generation.

Findings

Both orderings produce Gray codes for specific sequence sets

Efficient algorithms are developed for sequence generation

Comparative analysis of the generated sequences is provided

Abstract

We consider two order relations: that induced by the m-ary reflected Gray code and a suffix partitioned variation of it. We show that both of them when applied to some sets of restricted growth sequences still yield Gray codes. These sets of sequences are: subexcedant or ascent sequences, restricted growth functions, and staircase words. In each case we give efficient exhaustive generating algorithms and compare the obtained results.