N-realizable Quadruple

• Main Authors: Kuei-Ying Liu, 劉桂瑛
• Other Authors: Chiang Lin
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/37kc7y

碩士 === 國立中央大學 === 數學研究所 === 94 === For n,k $in$ N, a nondecreasing sequence of positive integers m1,m2,...,mk is said to be n-realizable if {1,2,...,n} can be partitioned into k mutually disjoint subsets S1,S2,...,Sk such that $sumlimits_{x in S_i}x=m_i$ for each $1 leq i leq k$. In this paper, we give a necessary and sufficient condition for a nondecreasing sequence of four positive integers to be n-realizable.