Sets of block structure and discrepancy estimates
Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 2, pp. 337-349.

Soient 𝐱=(x n ) n∈ℕ une suite d'éléments d'un ensemble fini M et 𝐟 = (f n ) n∈ℕ une suite d'applications f n :M→M. Quelle information sur 𝐱 et 𝐟 permet d'obtenir des estimations de la discrépance de la suite 𝐟(𝐱)=(f n (x n )) n∈ℕ ? Nous donnons dans cet article des réponses à cette question, en utilisant un résultat qualitatif récent.

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

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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},
     volume = {9},
     number = {2},
     year = {1997},
     zbl = {0899.11036},
     mrnumber = {1617402},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1997__9_2_337_0/}
}
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Reinhard Winkler. Sets of block structure and discrepancy estimates. Journal de théorie des nombres de Bordeaux, Tome 9 (1997) no. 2, pp. 337-349. https://jtnb.centre-mersenne.org/item/JTNB_1997__9_2_337_0/

[D-T] M. Drmota and R.F. Tichy. Sequences, discrepancy and applications. Springer, Lecture Notes in Mathematics 1651 (1997). | MR | Zbl

[G] M. Goldstern. The complexity of uniform distribution. Math. Slovaca 44.5 (1994), 491-500. | EuDML | MR | Zbl

[H] E. Hlawka. Theorie der Gleichverteilung. Bibl. Inst. Mannheim - Wien- Zürich, 1979. | MR | Zbl

[Ki-Li] H. Ki and T. Linton. Normal numbers and subsets of N with given densities. Fund. Math. 144 (1994), 163-179. | EuDML | MR | Zbl

[Kui-N] L. Kuipers and H. Niederreiter. Uniform distribution of sequences. John Wiley and Sons, New York, 1974. | MR | Zbl

[Lo] V. Losert. Almost constant sequences of transformations. Mh. Math. 85 (1978), 105-113. | EuDML | MR | Zbl

[Lo-Ri] V. Losert and H. Rindler. Almost constant sequences. Soc. Math. de France Astérisque 61 (1979), 133-143. | MR | Zbl

[Rau] G. Rauzy. Etude de quelques ensembles de fonctions définis par des proprietés de moyenne. Théorie des Nombres Univ. de Bordeaux 1972/73, Exp. 20. | EuDML | MR | Zbl

[Ri] H. Rindler. Fast konstante Folgen. Acta Arith. 35.2 (1979), 189-193. | EuDML | MR | Zbl

[W] R. Winkler. Distribution preserving sequences of maps and almost constant sequences on finite sets. To appear in Mh. Math. | EuDML | MR | Zbl