# On Number Of Partitions Of An Integer Into A Fixed Number Of Positive Integers

 dc.contributor.author Oruc, A. Yavuz dc.date.accessioned 2015-05-27T12:20:44Z dc.date.available 2015-05-27T12:20:44Z dc.date.issued 2015-04 dc.identifier https://doi.org/10.13016/M2J62F dc.identifier.uri http://hdl.handle.net/1903/16351 dc.description Submitted to Journal of Number Theory. en_US dc.description.abstract This paper focuses on the number of partitions of a positive integer $n$ into $k$ positive summands, where $k$ is an integer between $1$ and $n$. Recently some upper bounds were reported for this number in [Merca14]. Here, it is shown that these bounds are not as tight as an earlier upper bound proved in [Andrews76-1] for $k\le 0.42n$. A new upper bound for the number of partitions of $n$ into $k$ summands is given, and shown to be tighter than the upper bound in [Merca14] when $k$ is between $O(\frac{\sqrt{n}}{\ln n})$ and $n-O(\frac{\sqrt{n}}{\ln n})$. It is further shown that the new upper bound is also tighter than two other upper bounds previously reported in~[Andrews76-1] and [Colman82]. A generalization of this upper bound to number of partitions of $n$ into at most $k$ summands is also presented. en_US dc.subject Partition theory en_US dc.subject Restricted partitions en_US dc.subject Upper bound en_US dc.title On Number Of Partitions Of An Integer Into A Fixed Number Of Positive Integers en_US dc.type Other en_US dc.relation.isAvailableAt A. James Clark School of Engineering en_us dc.relation.isAvailableAt Electrical & Computer Engineering en_us dc.relation.isAvailableAt Digital Repository at the University of Maryland en_us dc.relation.isAvailableAt University of Maryland (College Park, MD) en_us
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