论文标题

真正的Hardy Ramanujan公式会站起来吗?

Will the real Hardy-Ramanujan formula please stand up?

论文作者

DeSalvo, Stephen

论文摘要

$ n $整数分区数量的Hardy-Ramanujan公式是分区理论中最受欢迎的结果之一。尽管未遗漏的最终公式已被庆祝为反映其作者的天才,但它已经太普遍了,无法归因于某些不那么巧妙的简化版本,或者是其他作者随后扩展的更优雅的版本。我们试图提供一个明确而令人信服的理由,以区分各种公式和简化,并在最后一部分中汇总了关键接管列表。

The Hardy-Ramanujan formula for the number of integer partitions of $n$ is one of the most popular results in partition theory. While the unabridged final formula has been celebrated as reflecting the genius of its authors, it has become all too common to attribute either some simplified version of the formula which is not as ingenious, or an alternative more elegant version which was expanded on afterwards by other authors. We attempt to provide a clear and compelling justification for distinguishing between the various formulas and simplifications, with a summarizing list of key take-aways in the final section.

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