Difference operators for functions of partitions and its application to hook-content identities
主 题: Difference operators for functions of partitions and its application to hook-content identities
报告人: 熊欢 博士 (Université de Strasbourg)
时 间: 2017-01-12 15:30-16:15
地 点: 镜春园78号院，77201会议室
摘要： Partitions of integers arise naturally in combinatorics, number theory and representation theory. Recently, many results on the Plancherel averages of certain functions of partitions have been derived by Nekrasov, Okounkov, Han, Stanley and Petreolle. Motivated by the work of Stanley and Olshanski, several difference operators on functions of partitions are introduced and studied in this talk. As an application, we establish a formal method to compute Plancherel averages related to hook lengths and contents of partitions. Many new hook-content formulas are obtained and several classical results, such as Han-Stanley Theorem, are generalized by this method. Furthermore, we extend this idea to the sets of strict partitions, self-conjugate partitions and doubled distinct partitions respectively, therefore derive several Plancherel average type formulas in such cases.