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ON THE EXPANSIONS OF REAL NUMBERS IN TWO INTEGER BASESopen access
- Authors
- Bugeaud, Yann; Kim, Dong Han
- Issue Date
- 2017
- Publisher
- ANNALES INST FOURIER
- Keywords
- Combinatorics on words; Sturmian word; complexity; integer base expansion; continued fraction
- Citation
- ANNALES DE L INSTITUT FOURIER, v.67, no.5, pp 2225 - 2235
- Pages
- 11
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- ANNALES DE L INSTITUT FOURIER
- Volume
- 67
- Number
- 5
- Start Page
- 2225
- End Page
- 2235
- ISSN
- 0373-0956
1777-5310
- Abstract
- Let r and s be multiplicatively independent positive integers. We establish that 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}, respectively, cannot have simultaneously a low block complexity. In particular, they cannot be both Sturmian words.
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Related Researcher
- Kim, Dong Han
- College of Education (Department of Mathematics Education)