报告人: 韩国牛 教授 （法国Strasbourg大学）

时  间: 2018年5月28日  上午10：30-11：30

地  点: 理科楼LA106

摘  要:Integer partitions were first studied by Euler.

    The Ferrers diagram of an integer partition is a very useful tool for visualizing partitions.A Ferrers diagram is turned into a Young tableau by filling each cell with a unique integer satisfying some conditions.The number of Young tableaux is given by the famous hook length formula,discovered by Frame-Robinson-Thrall.

In this talk, we introduce the hook length expansion technique and explain how to find old and new hook length formulas for integer partitions. In particular, we derive an expansion formula for the powers of the Euler Product in terms of hook lengths, which is also discovered by Nekrasov-Okounkov and Westburg. We obtain an extension by adding two more parameters. It appears to be a discrete interpolation between the Macdonald identities and the generating function for t-cores.Several other summations involving hook length,

in particular, the Okada-Panova formula, will also be discussed.

报告人简介:韩国牛教授1992年获法国Strasbourg大学博士学位，师从组合学法国学派的领军人物之一Foata教授。现为法国国家科研中心（Centre National de la Recherche Scientifique,CNRS）副研究员（chargé de recherché）及南开大学讲席教授。主要研究领域为组合数学，已在Adv. Math., Trans. AMS等期刊发表高质量学术论文100篇。韩国牛教授对词和排列上的统计等分布问题有浓厚的兴趣，并取得了一系列重要成果。一个有关Z统计的组合证明获得了著名组合数学家Doron Zeilberger的个人奖励。他在研究Den统计量的过程中，提出了一种对排列的编码方法，得到组合数学界的广泛关注，其结果被当代巨擘Donald E. Knuth所著的理论计算机领域的权威著作The Art of Computer Programming收录。韩国牛教授的具体研究方向还包括q级数、形式计算、对称函数等。在生物数学和图像处理等跨学科领域也取得了一些成果。

学院联系人: 傅士硕

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