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【北航数学论坛】_Combinatorics on integer partitions_HAN GUONIU 研究员
ag平台网址:2017-06-09  浏览量:



Abstract: Integer partitions were first studied by Euler.

In the first part of this talk, I shall 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 discovered by Nekrasov-Okounkov and Westburg.Then, we prove that the Plancherel average of the even power sum of hook or content lengths is always a polynomial for certain classes of integer partitions, such as strict, doubled distinct and self-conjugate partitions.Finally, we mention the link with the limit shape conjecture for strict partition.

报告人概况: 1987年武汉大学毕业后到法国攻读博士学位, 之后成为法国国家科研中心的研究员,在法国斯特拉斯堡大学的数学研究所工作。国际著名组合专家,研究方向为组合计数理论,在组合双射理论取得系列重要成果,最近在整数分拆和Hankel行列式零点等问题的研究上也取得了重要进展。共发表论文九十余篇,最近三年发表论文十余篇。


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