p（N）的Hardy-Ramanujan-Rademacher公式的简单替代
Simple alternative to the Hardy-Ramanujan-Rademacher formula for p(N)
摘要：
最近的一篇论文研究了整数分区序列的全局结构，并通过组合分析使用模块化算术，得出了一个封闭的形式表达的映射从（N，M）的所有分区的一个正整数N到正好M个正整数和。IPS映射的输出是具有M列和等于p[N，M]的行数的“矩阵”，p[N，M]是将N划分为M个部分的数量。整数分割序列的全局结构是一棵复杂的树。在本文中，我们研究的IPS树的结构，并通过计数的有向路径通过树的数量，得到一个简单的公式，给出了，在封闭的形式，总的分区N到正好M部分的数量。通过在M上求和，我们得到了p（N）的Hardy-Ramanujan-Rademacher公式的一个透明替代。
英文摘要：
A recent paper examined the global structure of integer partitions sequences and, via combinatorial analysis using modular arithmetic, derived a closed form expression for a map from (N, M) to the set of all partitions of a positive integer N into exactly M positive integer summands. The output of the IPS map was a "matrix" having M columns and a number of rows equal to p[N, M], the number of partitions of N into M parts. The global structure of integer partition sequences (IPS) is that of a complex tree. In this paper, we examine the structure of the IPS tree and, by counting the number of directed paths through the tree, obtain a simple formula which gives, in closed form, the total number of partitions of N into exactly M parts. By summing over M, we obtain a transparent alternative to the Hardy-Ramanujan-Rademacher formula for p(N).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
