Sets of block structure and discrepancy estimates
Journal de Théorie des Nombres de Bordeaux, Volume 9 (1997) no. 2, pp. 337-349.

Given a sequence $𝐱={\left({x}_{n}\right)}_{n\in ℕ}$ on the finite set $M$ and a sequence $𝐟$ = ${\left({f}_{n}\right)}_{n\in ℕ}$ of maps ${f}_{n}:M\to M.$ Which information about $𝐱$ and $𝐟$ is suitable for getting estimates for the discrepancy of the sequence $𝐟\left(𝐱\right)={\left({f}_{n}\left({x}_{n}\right)\right)}_{n\in ℕ}$? The paper's object is, using a recent qualitative result, to give answers to this question.

Soient $𝐱={\left({x}_{n}\right)}_{n\in ℕ}$ une suite d'éléments d'un ensemble fini $M$ et $𝐟$ = ${\left({f}_{n}\right)}_{n\in ℕ}$ une suite d'applications ${f}_{n}:M\to M.$ Quelle information sur $𝐱$ et $𝐟$ permet d'obtenir des estimations de la discrépance de la suite $𝐟\left(𝐱\right)={\left({f}_{n}\left({x}_{n}\right)\right)}_{n\in ℕ\phantom{\rule{-0.166667em}{0ex}}}$? Nous donnons dans cet article des réponses à cette question, en utilisant un résultat qualitatif récent.

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author = {Reinhard Winkler},
title = {Sets of block structure and discrepancy estimates},
journal = {Journal de Th\'eorie des Nombres de Bordeaux},
pages = {337--349},
publisher = {Universit\'e Bordeaux I},
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language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.206/}
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Reinhard Winkler. Sets of block structure and discrepancy estimates. Journal de Théorie des Nombres de Bordeaux, Volume 9 (1997) no. 2, pp. 337-349. doi : 10.5802/jtnb.206. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.206/

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