## Partition of a Set of Integers into Subsets with Prescribed Sums

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 … Read more