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.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.identifier | https://doi.org/10.13016/M2J62F | |
| dc.identifier.uri | http://hdl.handle.net/1903/16351 | |
| 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 |
| 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 |