关于整数分拆的Alavi猜想的证明

A Proof of the Alavi Conjecture on Integer Decomposition

Ｙ．Ａｌａｖｉ，Ｐ．Ｅｒｄｓ等人在［１］中提出猜想：设自然数α＿１，α＿２…α＿ｋ满足且，则可以划分成ｋ个互不相交子集Ｓ＿１，Ｓ＿２，···，Ｓ＿ｋ，满足．本文证明了这个猜想。

Y. Alavi,P. Erds and others [1] have proposed a conecture:Let α_1,α_2,…,α_k be positive integers such that and Then S={1,2,…,n}can be partitioned into k disjoint subsets S_1,S_2, …,S_k,such that for each i We prove that the conjecture is true.