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ON THE EXPANSIONS OF REAL NUMBERS IN TWO MULTIPLICATIVELY DEPENDENT BASES
- Authors
- Bugeaud, Yann; Kim, Dong Han
- Issue Date
- Jun-2017
- Publisher
- CAMBRIDGE UNIV PRESS
- Keywords
- combinatorics on words; Sturmian word; complexity; b-ary expansion
- Citation
- BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, v.95, no.3, pp 373 - 383
- Pages
- 11
- Indexed
- SCIE
SCOPUS
- Journal Title
- BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY
- Volume
- 95
- Number
- 3
- Start Page
- 373
- End Page
- 383
- ISSN
- 0004-9727
1755-1633
- Abstract
- Let r >= 2 and s >= 2 be multiplicatively dependent integers. We establish a lower bound for the sum of the block complexities of 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.
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Related Researcher
- Kim, Dong Han
- College of Education (Department of Mathematics Education)