Automatic sequences based on Parry or Bertrand numeration systems
نویسندگان
چکیده
منابع مشابه
Bertrand Numeration Systems and Recognizability
There exist various well-known characterizations of sets of numbers recognizable by a nite automaton, when they are represented in some integer base p 2. We show how to modify these characterizations, when integer bases p are replaced by linear numeration systems whose characteristic polynomial is the minimal polynomial of a Pisot number. We also prove some related interesting properties.
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Let N denote the set of positive integers. Every sequence B = (b0, b1, . . .) of numbers in N satisfying (1) 1 = b0 < b1 < . . . is a basis for N, as each n in N has a B-representation (2) n = c0b0 + c1b1 + . . .+ ckbk, where bk ≤ n < bk+1 and the coefficients ci are given by the division algorithm: (3) n = ckbk + rk, ck = [n/bk], 0 ≤ rk < bk and (4) ri = ci−1bi−1 + ri−1, ci−1 = [ri/bi−1], 0 ≤ ...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2019
ISSN: 0196-8858
DOI: 10.1016/j.aam.2019.03.003