ON the EXPANSIONS of REAL NUMBERS in TWO MULTIPLICATIVELY DEPENDENT BASES

Yann Bugeaud, Dong Han Kim

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let r ≥ and s ≥ 2 be multiplicatively dependent integers. We establish a lower bound for the sum of the block complexities of the -ary expansion and the r-ary expansion and the s-ary expansion of an irrational real number, viewed as infinite words on {0, 1,...,r - 1} and {0, 1,...,s - 1}, and we show that this bound is best possible.

Original languageEnglish
Pages (from-to)373-383
Number of pages11
JournalBulletin of the Australian Mathematical Society
Volume95
Issue number3
DOIs
StatePublished - 1 Jun 2017

Keywords

  • b-ary expansion
  • combinatorics on words
  • complexity
  • Sturmian word

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