Contents

Ars Combinatoria

  • Research article

There are Binary Circular Cube-Free Words of Length \(n\) Contained Within the Thue-Morse Word for all Positive Integers \(n\).

D.Sean Fitzpatrick1
1Department of Mathematics and Statistics University of Winnipeg Winnipeg, Manitoba R3B 2E9, Canada
  • Published: 31/01/2005

Abstract

We extend the work of Currie and Fitzpatrick [1] on circular words avoiding patterns by showing that, for any positive integer \(n\), the Thue-Morse word contains a subword of length \(n\) which is circular cube-free. This proves a conjecture of V. Linek.

Information
Guidelines
CP Initiatives
Follow CP
Facebook X-twitter Linkedin

1970-2025 CP (Manitoba, Canada) unless otherwise stated.

Citation
D.Sean Fitzpatrick. There are Binary Circular Cube-Free Words of Length \(n\) Contained Within the Thue-Morse Word for all Positive Integers \(n\).[J], Ars Combinatoria, Volume 074. 323-329. .