Abstract
Let R(n, a) denote the number of unrestricted partitions of n whose subsums are all different of a, and Q(n, a) the number of unequal partitions (i.e. each part is allowed to occur at most once) with the same property. In a preceding paper, we considered R(n,a) and Q(n,a) for \( a\, \geqslant \,{\lambda _1}\sqrt n \), where λ1 is a small constant. Here we study the case \( a\, \geqslant \,{\lambda _2}\sqrt n \). The behaviour of these quantities depends on the size of a, but also on the size of s(a), the smallest positive integer which does not divide a.
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Dedicated to Professor Paul T. Bateman for his seventieth birthday
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© 1990 Bikhäuser Boston
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Erdös, P., Nicolas, J.L., Sárközy, A. (1990). On the Number of Partitions of n Without a Given Subsum, II. In: Berndt, B.C., Diamond, H.G., Halberstam, H., Hildebrand, A. (eds) Analytic Number Theory. Progress in Mathematics, vol 85. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3464-7_14
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DOI: https://doi.org/10.1007/978-1-4612-3464-7_14
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