ON the EXPANSIONS of REAL NUMBERS in TWO MULTIPLICATIVELY DEPENDENT BASES

Yann Bugeaud; Dong Han Kim

doi:10.1017/S0004972716001040

ON the EXPANSIONS of REAL NUMBERS in TWO MULTIPLICATIVELY DEPENDENT BASES

Yann Bugeaud
, Dong Han Kim

Department of Mathematics Education

Université de Strasbourg

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	373-383
Number of pages	11
Journal	Bulletin of the Australian Mathematical Society
Volume	95
Issue number	3
DOIs	https://doi.org/10.1017/S0004972716001040
State	Published - 1 Jun 2017

Keywords

Sturmian word
b-ary expansion
combinatorics on words
complexity

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10.1017/S0004972716001040

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title = "ON the EXPANSIONS of REAL NUMBERS in TWO MULTIPLICATIVELY DEPENDENT BASES",

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.",

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author = "Yann Bugeaud and Kim, \{Dong Han\}",

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N2 - 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.

AB - 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.

KW - Sturmian word

KW - b-ary expansion

KW - combinatorics on words

KW - complexity

UR - https://www.scopus.com/pages/publications/85000384311

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IS - 3

ER -

ON the EXPANSIONS of REAL NUMBERS in TWO MULTIPLICATIVELY DEPENDENT BASES

Abstract

Keywords

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