The direct product of two words is a naturally defined word on the alphabet of pairs of symbols. An infinite word is uniformly recurrent if each its subword occurs in it with bounded gaps. An infinite word is strongly recurrent if the direct product of it with each uniformly recurrent word is also uniformly recurrent. We prove that fixed points of the expanding binary symmetric morphisms are strongly recurrent. In particular, such is the Thue-Morse word.

Source : oai:HAL:hal-00990432v1

Volume: Vol. 12 no. 4

Published on: January 1, 2010

Submitted on: March 26, 2015

Keywords: infinite words,uniform recurrence,strong recurrence,symmetric morphisms,Thue-Morse word,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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