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将一个自然数n表示为若干个自然数之和的形式 n=n_1+n_2+…+n_r(n_r∈N,r=1,2,…)(1)那么{n_1,n_2,…,n_r}称为k的一个分拆,如果不计加数的顺序,就称为无序分拆,简称分拆. 对于无序分拆,常假定n_1≥n_2≥…≥n_r,即加数由大到小排列,在这条件下(1)的解数P(n)称为分拆数。分拆的种种问题,曾是堆垒数论的一个古老课题,近年又成为组合数学的一个“热门话题”,
A natural number n is expressed as a sum of a number of natural numbers n=n_1+n_2+...+n_r(n_r∈N,r=1,2,...) (1) Then {n_1,n_2,...,n_r} is called k. A spin-off, if excluding the order of the addends, is called an unordered split, or abbreviation split. For an unordered spin-off, it is often assumed that n_1≥n_2≥...≥n_r, that is, the addends are arranged from largest to smallest, Under this condition, the number of solutions P(n) of (1) is called the number of splits. The various problems of spin-offs were once an ancient subject of pile number theory, and in recent years it has become a “hot topic” in combinatorial mathematics.