Chen, Fulong; Fu, Hunglin; Wang, Yiju; Zhou, Jianqin Partition of a set of integers into subsets with prescribed sums. (English) Zbl 1093.11016 Taiwanese J. Math. 9, No. 4, 629-638 (2005). A nonincreasing sequence of positive integers \(\langle m_1, m_2, \ldots, m_k \rangle\) is said to be \(n\)-realizable if the set \(I_n = \{ 1, 2, \ldots, n\}\) can be partitioned into \(k\) mutually disjoint sunsets \(S_1, S_2, \ldots, S_k\) such that \(\sum_{x \in S_i} x = m_i\) for each \(i\), \(1 \leq i \leq k\).The authors show that if a nonincreasing sequence of positive integers \(\langle m_1, m_2, \ldots, m_k \rangle\) satisfies \(\sum_{i=1}^k m_i = \) \(n \choose 2\) and \(m_{k-1} \geq n\), then this sequence is \(n\)-realizable. Moreover, they illustrate that this result cannot be improved by replacing the latter condition with \(m_{k-2} \geq n\). Reviewer: Ortrud R. Oellermann (Winnipeg) Cited in 6 Documents MSC: 11B75 Other combinatorial number theory 90C35 Programming involving graphs or networks 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05A18 Partitions of sets Keywords:\(n\)-realizable; integers; partition of a set PDFBibTeX XMLCite \textit{F. Chen} et al., Taiwanese J. Math. 9, No. 4, 629--638 (2005; Zbl 1093.11016) Full Text: DOI