Optimization Online


Partition of a Set of Integers into Subsets with Prescribed Sums

Wang Yiju (yiju-66***at***263.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


Entry Submitted: 03/30/2003
Entry Accepted: 03/31/2003
Entry Last Modified: 04/02/2003

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Programming Society