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Sur les sous-sommes d’une partition. II. (On subsums of a partition. II). (French) Zbl 0684.10048

Let \(\Pi =\{a_ 1+a_ 2+...+a_ s=n\); \(a_ 1\geq a_ 2\geq...\geq a_ s>0\}\) be a generic partition of n where \(s=s(\Pi)\) and \(a_ j\) are integers. Each sum \(a_{i_ 1}+...+a_{i_ t}\) \((i_ 1<...<i_ t)\) is said to be a subsum of \(\Pi\). Let \(\Sigma\) (\(\Pi)\) be the set of integers representable by subsums of \(\Pi\). Let Q be a fixed finite set of positive integers, \(Q\neq \emptyset\). In Chapters IV and V of Part I (see the preceding review) the author proved asymptotic results for the number of partitions \(\Pi\) of n such that \(\Sigma (\Pi)\cap Q=\emptyset.\)
In the paper under review the author obtains more precise results for the number of partitions \(\Pi\) of n such that \(\Sigma (\Pi)\cap Q=\emptyset\) and \(\Sigma (\Pi)\supseteq Q'=\{1,2,3,...,\sup Q\}\setminus Q\) if \(Q'\) satisfies certain additivity conditions.
For Part III, see the following review.
Reviewer: M.Szalay

MSC:

11P81 Elementary theory of partitions
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