Partition of a set of integers into subsets with prescribed sums

Fu Long Chen*, Hung-Lin Fu, Yiju Wang, Jianqin Zhou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

A nonincreasing sequence of positive integers (m1, m 2, ⋯, mk) is said to be n-realizable if the set In = {1, 2, ⋯, n} can be partitioned into k mutually disjoint subsets S1, S2, ⋯, Sk such that ∑x∈si x = mi for each 1 ≤ i ≤ k. In this paper, we will prove that a nonincreasing sequence of positive integers (m 1, m2, ⋯, mk) is n-realizable under the conditions that ∑i=1 k mi = (n+1/2) and mk-1 ≥ n.

Original languageEnglish
Pages (from-to)629-638
Number of pages10
JournalTaiwanese Journal of Mathematics
Volume9
Issue number4
DOIs
StatePublished - 1 Jan 2005

Keywords

  • Graph decomposition
  • Integer partition
  • Partition

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