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On the parity of generalized partition functions, III

Fethi Ben Saïd; Jean-Louis Nicolas; Ahlem Zekraoui — 2010

Journal de Théorie des Nombres de Bordeaux

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.

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