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Combinatorics on integer partitions

Release time:June 13, 2017 / Siying He

Topic: Combinatorics on integer partitions      

Date: June 14 10 :00-11 :00      

Venue:Main Building Room 321      

Speaker : Han Guoniu      

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.

 

Bio of the Speaker: Han Guoniu was graduated from Wuhan University and pursued a doctor degree in France, After which he joined the France National Science Research Center. Recently, he has ben working in the university of Strasbourg.

 

Invited Researcher:Liang Xiangyu      

 

School of Mathematics and System Science