On the polynomial representation for the number of partitions with fixed length期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the polynomial representation for the number of partitions with fixed length

Authors:	So Ryoung Park Jinsoo Bae Hyun Gu Kang Iickho Song

Institution:	School of Information, Communications, and Electronics Engineering, The Catholic University of Korea, Bucheon 420-743 Korea ; Department of Information and Communication Engineering, Sejong University, Seoul 143-747 Korea ; Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology, Daejeon 305-701 Korea ; Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology, Daejeon 305-701 Korea

Abstract:	In this paper, it is shown that the number of partitions of a nonnegative integer with parts can be described by a set of $\widetilde{k}$ polynomials of degree in $Q_{\widetilde{k}}$ , where $\widetilde{k}$ denotes the least common multiple of the integers $1, 2, \cdots, k$ and $Q_{\widetilde{k}}$ denotes the quotient of when divided by $\widetilde{k}$ . In addition, the sets of the $\widetilde{k}$ polynomials are obtained and shown explicitly for and .

Keywords:	Partition polynomial representation nonrecursive formula

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