Numeration Systems, Linear Recurrences, and Regular Sets
نویسندگان
چکیده
منابع مشابه
Numeration Systems, Linear Recurrences, and Regular Sets
A numeration system based on a strictly increasing sequence of positive integers u0 = 1, u1, u2, . . . expresses a non-negative integer n as a sum n = ∑i j=0 ajuj . In this case we say the string aiai−1 · · · a1a0 is a representation for n. If gcd(u0, u1, . . .) = g, then every sufficiently large multiple of g has some representation. If the lexicographic ordering on the representations is the ...
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Additive numeration systems and the corresponding additive arithmetic functions have been studied from various points of view since the seminal papers of H. Delange [4, 5], where such functions were investigated for the usual q-adic numeration system. Later more exotic systems of numeration, such as general linear numeration systems [13, 14], especially such systems defined by linear recurring ...
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with digits δl{0, 1} for 0 ≤ l ≤ L, where the digits are computed by the greedy algorithm: there is a unique integer L such that GL ≤ n < GL+1. Then n can be written as n = δLGL + nL with 0 ≤ nL < GL and by iterating this procedure with nL the expansion (1.3) is obtained. An extensive description of digital expansions with respect to linear recurring base sequences is given in [15, 19, 20, 21]....
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ژورنال
عنوان ژورنال: Information and Computation
سال: 1994
ISSN: 0890-5401
DOI: 10.1006/inco.1994.1076