关于正整数分拆数p(n)的历史注记
A HISTORICAL NOTE ON PARTITION NUMBER p(n) OF INTEGER</em>
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<p class='author'><strong>作 者：</strong><a href='/writer/article.aspx?id=100000012231182' target='_blank' ><b class='type_ico_id'></b></a><a href='/zk/search.aspx?key=A%3d%5b%e7%bd%97%e8%a7%81%e4%bb%8a%5d' title='罗见今[1]'>罗见今[1]</a> <a href='/writer/article.aspx?id=100000005907535' target='_blank' ><b class='type_ico_id'></b></a><a href='/zk/search.aspx?key=A%3d%5b%e7%8e%8b%e6%b5%b7%e6%9e%97%5d' title='王海林[2]'>王海林[2]</a> <em> </em></p><p class='organ'><strong>机构地区：</strong><a href='/organ/article.aspx?id=53520&subid=&showname=&searchtype=' target='_blank'><b class='type_ico_id'></b></a><a href='/zk/search.aspx?key=S%3d%e5%86%85%e8%92%99%e5%8f%a4%e5%b8%88%e8%8c%83%e5%a4%a7%e5%ad%a6%e7%a7%91%e5%ad%a6%e5%8f%b2%e4%b8%8e%e7%a7%91%e6%8a%80%e7%ae%a1%e7%90%86%e7%b3%bb' title='[1]内蒙古师范大学科学史与科技管理系,内蒙古呼和浩特010022'>[1]内蒙古师范大学科学史与科技管理系,内蒙古呼和浩特010022</a> <a href='/organ/article.aspx?id=2566&subid=&showname=&searchtype=' target='_blank'><b class='type_ico_id'></b></a><a href='/zk/search.aspx?key=S%3d%e7%a9%ba%e5%86%9b%e9%9b%b7%e8%be%be%e5%ad%a6%e9%99%a2%e6%95%b0%e5%ad%a6%e6%95%99%e7%a0%94%e5%ae%a4' title='[2]空军雷达学院数学教研室,湖北武汉430010'>[2]空军雷达学院数学教研室,湖北武汉430010</a> <em> </em></p><p class='from'><strong>出 处：</strong><a href='/journal/summary.aspx?gch=95820X' target='_blank'><b class='type_ico_id'></b></a><a href='/zk/search.aspx?key=J%3d%5b%e5%86%85%e8%92%99%e5%8f%a4%e5%b8%88%e8%8c%83%e5%a4%a7%e5%ad%a6%e5%ad%a6%e6%8a%a5%ef%bc%88%e8%87%aa%e7%84%b6%e7%a7%91%e5%ad%a6%e6%b1%89%e6%96%87%e7%89%88%ef%bc%89%5d' title='内蒙古师范大学学报（自然科学汉文版）'>《内蒙古师范大学学报（自然科学汉文版）》</a>2002年第3期290-295,共6页<em>Journal of Inner Mongolia Normal University(Natural Science Edition)</em></p><p class='fund'><strong>基 金：</strong>天元(国家自然科学数学)基金数学史方向资助项目"近代数学史研究</p><p class='abstrack'><strong>摘 要：</strong>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.<em><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.</em></p><p class='subject'><strong>关 键 词：</strong><a href='/subject/article.aspx?id=1450931' target='_blank'><b class='type_ico_id'></b></a><a href='/zk/search.aspx?key=K%3d%5b%e6%ad%a3%e6%95%b4%e6%95%b0%5d' title='正整数'>正整数</a> <a href='/subject/article.aspx?id=6750810' target='_blank'><b class='type_ico_id'></b></a><a href='/zk/search.aspx?key=K%3d%5b%e5%88%86%e6%8b%86%e6%95%b0%5d' title='分拆数'>分拆数</a> <a href='/subject/article.aspx?id=3628517' target='_blank'><b class='type_ico_id'></b></a><a href='/zk/search.aspx?key=K%3d%5b%e7%bb%84%e5%90%88%e8%ae%a1%e6%95%b0%5d' title='组合计数'>组合计数</a> <a href='/subject/article.aspx?id=1432414' target='_blank'><b class='type_ico_id'></b></a><a href='/zk/search.aspx?key=K%3d%5b%e6%95%b4%e6%95%b0%e5%88%86%e6%8b%86%5d' title='整数分拆'>整数分拆</a> <a href='/zk/search.aspx?key=K%3d%5bp(n)%e4%bc%b0%e5%80%bc%5d' title='p(n)估值'>p(n)估值</a> <a href='/zk/search.aspx?key=K%3d%5b%e6%95%b0%e8%ae%ba%5d' title='数论'>数论</a> <a href='/zk/search.aspx?key=K%3d%5b%e7%bb%84%e5%90%88%e6%95%b0%e5%ad%a6%5d' title='组合数学'>组合数学</a> <a href='/zk/search.aspx?key=K%3d%5b%e9%80%bc%e8%bf%91%e8%ae%ba%5d' title='逼近论'>逼近论</a> </p><p class='class'><strong>分 类 号：</strong><a href='/zk/search.aspx?key=C%3dO156.1' title='O156.1'>O156.1</a>[<a href = '/domain/article.aspx?id=378' >理学—数学</a>] <a href='/zk/search.aspx?key=C%3dO157' title='O157'>O157</a>[<a href = '/domain/article.aspx?id=379' >理学—基础数学</a>] </p>
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