On Uniform Recurrence of a Direct Product

A direct product of two words is a naturally defined word on the alphabet of pairs of symbols. We introduce the class URP of uniformly recurrent words such that a direct product of any its member and each uniformly recurrent word is also uniformly recurrent. This class is proved to contain all fixed points of expanding binary symmetric morphisms. In particular, the Thue-Morse word is in URP.

• Type: Journal
• Year: 2010
• Where: DMTCS
• Authors: Pavel Vadimovich Salimov
• Keywords: Binary Symmetric Morphisms, Direct Product, DMTCS 2010, Recurrent Word, Sensor Networks