Let a be an irrational number with 0 < a < 1. Using the continued fraction expansion of a, the class of a-words is introduced. It contains certain sequences of words that are known to relate to the characteristic sequence f(a) of a. When a = (v'~-1)/2, a-words are precisely the Fibonacci words. In t
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Unbordered factors of the characteristic sequences of irrational numbers
β Scribed by Wai-fong Chuan
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 439 KB
- Volume
- 205
- Category
- Article
- ISSN
- 0304-3975
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Let CL be an irrational number between 0 and 1 with continued fraction [0, al + 1,~. .]. The characteristic sequence of x is by definition an infinite word f over the alphabet (0. 1 }, whose nth letter is [(n + 1)cx -ncr], n > 1. A.A. Markov has proved that f has a representation ~'=uIu~..., where