A trace partitioned Gray code for q-ary generalized Fibonacci strings

TL;DR

This paper introduces a trace partitioned Gray code for q-ary strings avoiding k consecutive identical symbols, extending previous binary string results and considering the parity of q for its construction.

Contribution

It presents a novel Gray code construction for q-ary strings avoiding specific patterns, generalizing binary string Gray codes and accounting for q's parity.

Findings

Provides a Gray code for q-ary strings avoiding k consecutive equal symbols

Generalizes binary string Gray codes to q-ary case

Offers two constructions based on q's parity

Abstract

We provide a trace partitioned Gray code for the set of q-ary strings avoiding a pattern constituted by k consecutive equal symbols. The definition of this Gray code is based on two different constructions, according to the parity of q. This result generalizes, and is based on, a Gray code for binary strings avoiding k consecutive 0's.