| 摘要: | n,k為自然數，一個非遞減正整數序列m1,m2,...,mk，我們稱它為n-realizable，如果{1,2,...,n}這個正整數集合，可以被分割成k個互不相交的子集S1,S2,...,Sk，使得對於每一個$1 leq i leq k$，Si的元素和為mi。在這一篇論文裡面，我們主要得到：四個正整數是n- realizable的充分、必要條件。 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. |
