An alternative construction of normal numbers
Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 1, p. 165-177
Nous construisons une nouvelle classe de nombres normaux en base b de manière récursive en utilisant des chemins eulériens dans une suite de digraphes de de Bruijn. Dans cette construction chaque chemin est fabriqué comme une extension du chemin précédent, de telle manière que le bloc b-adique déterminé par le chemin contienne le nombre maximal de sous-blocs b-adiques distincts de longueurs consécutives dans l’arrangement le plus compact. Toute source de redondance est évitée à chaque étape. Notre construction récursive est une alternative à plusieurs constructions par concaténation à la Champernowne qui sont bien connues.
A new class of b-adic normal numbers is built recursively by using Eulerian paths in a sequence of de Bruijn digraphs. In this recursion, a path is constructed as an extension of the previous one, in such way that the b-adic block determined by the path contains the maximal number of different b-adic subblocks of consecutive lengths in the most compact arrangement. Any source of redundancy is avoided at every step. Our recursive construction is an alternative to the several well-known concatenative constructions à la Champernowne.
@article{JTNB_2000__12_1_165_0,
     author = {Ugalde, Edgardo},
     title = {An alternative construction of normal numbers},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {1},
     year = {2000},
     pages = {165-177},
     zbl = {1015.11035},
     mrnumber = {1827846},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2000__12_1_165_0}
}
Ugalde, Edgardo. An alternative construction of normal numbers. Journal de théorie des nombres de Bordeaux, Tome 12 (2000) no. 1, pp. 165-177. http://www.numdam.org/item/JTNB_2000__12_1_165_0/

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