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 |
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Pages (from-to) | 373-383 |
Number of pages | 11 |
Journal | Bulletin of the Australian Mathematical Society |
Volume | 95 |
Issue number | 3 |
DOIs | |
State | Published - 1 Jun 2017 |
Keywords
- b-ary expansion
- combinatorics on words
- complexity
- Sturmian word