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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Partitions with congruence conditions


Author: M. M. Robertson
Journal: Proc. Amer. Math. Soc. 57 (1976), 45-49
MSC: Primary 10J20; Secondary 10A45
DOI: https://doi.org/10.1090/S0002-9939-1976-0404184-7
MathSciNet review: 0404184
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Abstract: Let $ A = \cup _{i = 1}^q\{ a(i) + \nu M:\nu = 0,1,2, \ldots \} $, where $ q,M$ and the $ a(i)$ are positive integers such that $ a(1) < a(2) < \cdots < a(q) \leqslant M$. Asymptotic formulae are obtained for $ p(n,k,A),{p^ \ast }(n,k,A)$ the number of partitions of $ n$ into $ k$ parts, $ k$ unequal parts respectively, where all the parts belong to $ A$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0404184-7
Keywords: Partition, asymptotic, congruence
Article copyright: © Copyright 1976 American Mathematical Society