N-realizable Quadruple
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 g...
| Main Authors: | , |
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| Format: | Others |
| Language: | en_US |
| Published: |
2006
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| Online Access: | http://ndltd.ncl.edu.tw/handle/37kc7y |
| Summary: | 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.
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