新等式推出任意条件下可重复组合的计数公式

The New Equation Deduces the Counting Formula of Repeatable Combination under Arbitrary Conditions

摘要: 可重复组合的计数是组合数学中的重要内容，几百年都未完全解决，任意条件下的计数公式应用容斥原理证明还存在争议，这里根据发现的一些新等式，推出了任意条件下可重复组合的计数公式，并指出类似的等式大量存在，根据等式给出的集合，分析了容斥原理证明此类问题的不足。根据推论给出了猜想。

Abstract: Repeatable combination counting is an important content in combinatorial mathematics that has not been solved for hundreds of years. It is still controversial to prove the counting formulas under arbitrary conditions by using principle of inclusion and exclusion. In this paper, according to some new equations found, the counting formulas of repeatable combination under arbitrary conditions are derived. It is pointed out that there are a lot of similar equations. According to the set given by equality, the deficiency of this kind of problem proved by the principle of inclusion and exclusion is analyzed. A conjecture is given on the basis of a corollary.