# Beckett-Gray Codes

• Published in 2016
In this paper we discuss a natural mathematical structure that is derived from Samuel Beckett's play "Quad". This structure is called a binary Beckett-Gray code. Our goal is to formalize the definition of a binary Beckett-Gray code and to present the work done to date. In addition, we describe the methodology used to obtain enumeration results for binary Beckett-Gray codes of order $n = 6$ and existence results for binary Beckett-Gray codes of orders $n = 7,8$. We include an estimate, using Knuth's method, for the size of the exhaustive search tree for $n=7$. 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.

### BibTeX entry

@article{BeckettGrayCodes,
title = {Beckett-Gray Codes},
abstract = {In this paper we discuss a natural mathematical structure that is derived
from Samuel Beckett's play "Quad". This structure is called a binary
Beckett-Gray code. Our goal is to formalize the definition of a binary
Beckett-Gray code and to present the work done to date. In addition, we
describe the methodology used to obtain enumeration results for binary
Beckett-Gray codes of order {\$}n = 6{\$} and existence results for binary
Beckett-Gray codes of orders {\$}n = 7,8{\$}. We include an estimate, using Knuth's
method, for the size of the exhaustive search tree for {\$}n=7{\$}. 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.},
url = {http://arxiv.org/abs/1608.06001v1 http://arxiv.org/pdf/1608.06001v1},
author = {Mark Cooke and Chris North and Megan Dewar and Brett Stevens},
comment = {},
urldate = {2016-08-24},
archivePrefix = {arXiv},
eprint = {1608.06001},
primaryClass = {math.CO},
year = 2016
}