Pavel Vadimovich Salimov - On uniform recurrence of a direct product

dmtcs:522 - Discrete Mathematics & Theoretical Computer Science, January 1, 2010, Vol. 12 no. 4 - https://doi.org/10.46298/dmtcs.522
On uniform recurrence of a direct productArticle

Authors: Pavel Vadimovich Salimov 1

  • 1 Sobolev Institute of Mathematics

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.


Volume: Vol. 12 no. 4
Published on: January 1, 2010
Imported 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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