关于正整数分拆数p(n)的历史注记

<title>A HISTORICAL NOTE ON PARTITION NUMBER p(n) OF INTEGER

正整数的分拆数p(n)及其估值是数论、组合数学讨论的一个重要问题,推动了数论、逼近论、生成函数变换、组合计数等的发展.按照组合计数和逼近的观点,讨论了p(n)几种估值的优劣,介绍了哈代、拉马努占等的杰出成果及在中国的影响.

<Abstrcat> Partition number p(n) of integer and its estimation is an important issue which is studies in both number theory and combinatorics.This problem has pushed forward theory of numbers,approximation,variation of generating function and combinatorial counting as well.This paper,in connection with the question appearing during teaching,discusses advantage and disadvantage of several p(n)s estimations from the view of combinatorial counting theory and approximation.At the same time,the remarkable achievement obtained by G H Hardy and S A Ramanujan is presented.The influence of their achievement on China is also discussed.