Some noiseless coding theorem connected with Havrda and Charvat and Tsallis's entropy

Satish Kumar; Rajesh Kumar

Displaying similar documents to “Some noiseless coding theorem connected with Havrda and Charvat and Tsallis's entropy”

Entropy numbers of certain summation operators.

Creutzig, J., Linde, W. (2001)

Georgian Mathematical Journal

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Entropy numbers of diagonal operators of logarithmic type.

Kühn, Thomas (2001)

Georgian Mathematical Journal

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Relations among arithmetical functions, automatic sequences, and sum of digits functions induced by certain Gray codes

Yuichi Kamiya, Leo Murata (2012)

Journal de Théorie des Nombres de Bordeaux

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In the study of the $2$ -adic sum of digits function $S_{2} (n)$ , the arithmetical function $u (0) = 0$ and $u (n) = {(- 1)}^{n - 1}$ for $n \geq 1$ plays a very important role. In this paper, we firstly generalize the relation between $S_{2} (n)$ and $u (n)$ to a bijective relation between arithmetical functions. And as an application, we investigate some aspects of the sum of digits functions $S_{𝒢} (n)$ induced by binary infinite Gray codes $𝒢$ . We can show that the difference of the sum of digits function, $S_{𝒢} (n) - S_{𝒢} (n - 1)$ , is realized by an automaton. And the summation formula...