A note on weight enumerators of linear self-dual codes.

Lomadze, N.

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Lomadze, G. (2001)

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Caragiu, Mihai (2005)

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Lomadze, G. (1998)

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On the parity of generalized partition functions, III

Fethi Ben Saïd, Jean-Louis Nicolas, Ahlem Zekraoui (2010)

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Improving on some results of J.-L. Nicolas [], the elements of the set $𝒜 = 𝒜 (1 + z + z^{3} + z^{4} + z^{5})$ , for which the partition function $p (𝒜, n)$ (i.e. the number of partitions of $n$ with parts in $𝒜$ ) is even for all $n \geq 6$ are determined. An asymptotic estimate to the counting function of this set is also given.

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...

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