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$0 - 1$ sequences having the same numbers of $(1 - 1)$ -couples of given distances

Antonín Lešanovský, Jan Rataj, Stanislav Hojek (1992)

Mathematica Bohemica

Let $a$ be a $0 - 1$ sequence with a finite number of terms equal to 1. The distance sequence $δ^{(a)}$ of $a$ is defined as a sequence of the numbers of $(1 - 1)$ -couples of given distances. The paper investigates such pairs of $0 - 1$ sequences $a, b$ that a is different from $b$ and $δ^{(a)} = δ^{(b)}$ .

14-term arithmetic progressions on quartic elliptic curves.

MacLeod, Allan J. (2006)

Journal of Integer Sequences [electronic only]

3 arten von Linearverbindungen bei Bernoullipolynomen

I. Paasche (1972)

Matematički Vesnik

...-Expansions, Linear Recurrences, and the Sum-of-Digits Function.

Robert F. Tichy, Peter J. Grabner (1991)

Manuscripta mathematica

ℚ-linear relations of special values of the Estermann zeta function

Makoto Ishibashi (1998)

Acta Arithmetica

Łukasiewicz language and diagonals of formal series. (Langage de Łukasiewicz et diagonales de séries formelles.)

Fagnot, Isabelle (1996)

Journal de Théorie des Nombres de Bordeaux

(Non-)weakly mixing operators and hypercyclicity sets

Frédéric Bayart, Étienne Matheron (2009)

Annales de l’institut Fourier

We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space $ℓ^{1} (ℕ)$ , any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for $c_{0} (ℕ)$ or $ℓ^{p} (ℕ)$ , $1 < p < \infty$ . Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.

[unknown]

Pelesko, John A. (2004)

Journal of Integer Sequences [electronic only]

$β$ -shift, systèmes de numération et automates

Nathalie Loraud (1995)

Journal de théorie des nombres de Bordeaux

In this note we prove that the language of a numeration system is the language of a $_{β}$ -shift under some assumptions on the basis. We deduce from this result a partial answer to the question when the language of a numeration system is regular. Moreover, we give a characterization of the arithmetico-geometric sequences and the mixed radix sequences that are basis of a numeration system for which the language is regular. Finally, we study the Ostrowski systems of numeration and give another proof of...