On partitions ofN into summands coprime toN

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چکیده

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On the enumeration of partitions with summands in arithmetic progression

Enumerating formulae are constructed which count the number of partitions of a positive integer into positive summands in arithmetic progression with common difference D. These enumerating formulae (denoted pD(n)) which are given in terms of elementary divisor functions together with auxiliary arithmetic functions (to be defined) are then used to establish a known characterisation for an intege...

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The factor c−1 √ n log n is nothing but the asymptotic value of the mean number of summands in a random partition of n, each partition of n being equally likely; cf. [17]. Note that the number of partitions of n with m 1’s is given by p(n −m) − p(n −m − 1) for 0 ≤ m ≤ n; and, consequently, p(n−m) is nothing but the number of partitions of n which have ≥ m 1’s. Thus the factor one plays an impor...

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ژورنال

عنوان ژورنال: Aequationes mathematicae

سال: 1978

ISSN: 0001-9054,1420-8903

DOI: 10.1007/bf01818576