A note on Beckett-Gray codes and the relationship of Gray codes to data structures

TL;DR

This paper introduces binary Beckett-Gray codes inspired by Samuel Beckett's play, explores their enumeration for small sizes, and relates them to queue data structures, comparing with Gray codes realized by stacks.

Contribution

It defines a new mathematical structure called binary Beckett-Gray codes and analyzes their properties and realizations using queue data structures.

Findings

Enumerated all Beckett-Gray codes for n ≤ 6

Provided examples for n=7,8

Connected Gray codes to queue and stack data structures

Abstract

In this paper we introduce a natural mathematical structure derived from Samuel Beckett's play "Quad". We call this structure a binary Beckett-Gray code. We enumerate all codes for $n \leq 6$ and give examples for $n=7,8$. Beckett-Gray codes can be realized as successive states of a queue data structure. We show that the binary reflected Gray code can be realized as successive states of two stack data structures.