Uniform tag sequences

Cobham, Alan

doi:10.1007/bf01706087

Cited by 385 publications

(292 citation statements)

References 19 publications

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“…This condition is conveniently expressed in terms of digit substitutions (see [2], [6], [7]). The sequence a = {a n } is said to be a fixed point of a uniform ^-substitution if there is a rule which replaces each symbol of A by a string of k symbols of A, under which a is left fixed.…”

Section: Theorem (Loxton and Van Der Poorten) Let R>2 Be Fixed And Lmentioning

confidence: 99%

Digit patterns and transcendental numbers

Morton

Mourant

1991

J Aust Math Soc A

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We use a theorem of Loxton and van der Poorten to prove the transcendence of certain real numbers denned by digit patterns. Among the results we prove are the following. If k is an integer at least 2, P is any nonzero pattern of digits base k, and ep(n) € [0, r -1] counts the number of occurrences (mod r) of P in the base k representation of n , then '7(4'°) = J2T=o e p ) (")/ r " i s transcendental except when t = 3 , P = 1 and r = 2 . When (r, k -1) = 1 the linear span of the numbers n(e^) has infinite dimension over Q, where P ranges over all patterns base k without leading zeros.

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Section: Theorem (Loxton and Van Der Poorten) Let R>2 Be Fixed And Lmentioning

confidence: 99%

Digit patterns and transcendental numbers

Morton

Mourant

1991

J Aust Math Soc A

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“…In 1972, Cobham [5] However, most sequences are not k-automatic for any k. Instead of simply saying that a sequence is not k-automatic, we can measure quantitatively how "close" a sequence is to being k-automatic using the concept of automaticity studied in previous papers of the author and co-authors [26,27,20,10]. In addition to its evident intrinsic interest, automaticity has proved useful in obtaining nontrivial lower bounds in computational complexity theory; see [7,8,16,17].…”

Section: Introduction and Definitionsmentioning

confidence: 99%

“…Wagstaff [31] has provided a heuristic model that predicts that the least prime congruent to Proof. The fact that p is 2-automatic follows from the fact that the defining homomorphism p is 2-uniform; see [5].…”

Section: Introduction and Definitionsmentioning

confidence: 99%

Automaticity IV : sequences, sets, and diversity

Shallit¹

1996

Journal De Théorie Des Nombres De Bordeaux

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“…Furthermore, Cobham proved that the subword complexity of an automatic sequence is at most linear (see [16]). Hence, an easy consequence of those two results is the following.…”

Section: Algebraic Laurent Seriesmentioning

confidence: 99%

Subword complexity and finite characteristic numbers

Firicel¹

2010

Actes Des Rencontres Du CIRM

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Subword complexity and finite characteristic numbersAlina Firicel Abstract Decimal expansions of classical constants such as √ 2, π and ζ(3) have long been a source of difficult questions. In the case of finite characteristic numbers (Laurent series with coefficients in a finite field), where no carry-over difficulties appear, the situation seems to be simplified and drastically different. On the other hand, the theory of Drinfeld modules provides analogs of real numbers such as π, e or ζ values. Hence, it became reasonable to enquire how "complex" the Laurent representation of these "numbers" is.

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Uniform tag sequences

Cited by 385 publications

References 19 publications

Digit patterns and transcendental numbers

Digit patterns and transcendental numbers

Automaticity IV : sequences, sets, and diversity

Subword complexity and finite characteristic numbers

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