# An alternative construction of normal numbers

Journal de théorie des nombres de Bordeaux (2000)

- Volume: 12, Issue: 1, page 165-177
- ISSN: 1246-7405

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topUgalde, Edgardo. "An alternative construction of normal numbers." Journal de théorie des nombres de Bordeaux 12.1 (2000): 165-177. <http://eudml.org/doc/248514>.

@article{Ugalde2000,

abstract = {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.},

author = {Ugalde, Edgardo},

journal = {Journal de théorie des nombres de Bordeaux},

keywords = {-adic expansion; Eulerian cycles; Hamiltonian paths; -adic normal numbers; de Bruijn digraphs},

language = {eng},

number = {1},

pages = {165-177},

publisher = {Université Bordeaux I},

title = {An alternative construction of normal numbers},

url = {http://eudml.org/doc/248514},

volume = {12},

year = {2000},

}

TY - JOUR

AU - Ugalde, Edgardo

TI - An alternative construction of normal numbers

JO - Journal de théorie des nombres de Bordeaux

PY - 2000

PB - Université Bordeaux I

VL - 12

IS - 1

SP - 165

EP - 177

AB - 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.

LA - eng

KW - -adic expansion; Eulerian cycles; Hamiltonian paths; -adic normal numbers; de Bruijn digraphs

UR - http://eudml.org/doc/248514

ER -

## References

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