  


Partition of a Set of Integers into Subsets with Prescribed Sums
Wang Yiju (yiju66263.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 $m_{k1}\ge n$. 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: 03/30/2003 Modify/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  