- Partition of a Set of Integers into Subsets with Prescribed Sums Wang Yiju (yiju-66263.sina.com) Abstract: A nonincreasing sequence of positive integers $\langle m_1,m_2,\cdots,m_k \rangle$ is said to be {\em $n$-realizable\/} if the set $I_n=\{ 1,2,\cdots,n\}$ can be partitioned into $k$ mutually disjoint subsets $S_1,S_2,\cdots, S_k$ such that $\sum\limits_{x\in S_i}x=m_i$ for each $1\le i\le k$. In this paper, we will prove that a nonincreasing sequence of positive integers $\langle m_1,m_2,\cdots,m_k\rangle$ is $n$-realizable under the conditions that $\sum\limits_{i=1}^km_i={n+1\choose 2}$ and $m_{k-1}\ge n$. Keywords: Partition, Integer partition, Partite graph. Category 1: Combinatorial Optimization (Graphs and Matroids ) Citation: 1, Inst. of Opersearchs Research, Qufu Normal university, Rizhao Shandong, 276800, China, Mar, 2003 Download: Entry Submitted: 03/30/2003Entry Accepted: 03/31/2003Entry Last Modified: 04/02/2003Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.