On modifying constructed normal numbers

Bodo Volkmann

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The Pascal adic transformation is loosely Bernoulli

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Let $ℚ (α)$ be an algebraic number field given by the minimal polynomial $f$ of $α$ . We want to determine all subfields $ℚ (β) \subset ℚ (α)$ of given degree. It is convenient to describe each subfield by a pair $(g, h) \in ℤ [t] \times ℚ [t]$ such that $g$ is the minimal polynomial of $β = h (α)$ . There is a bijection between the block systems of the Galois group of $f$ and the subfields of $ℚ (α)$ . These block systems are computed using cyclic subgroups of the Galois group which we get from the Dedekind criterion. When a block system is known we compute the corresponding...

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An alternative construction of normal numbers

Edgardo Ugalde (2000)

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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...