报告人: 刘勇杉（重庆邮电大学）

日  期: 2019年10月12日

时  间: 14:40

地  点: 理科楼 LD202

摘  要: In 2007, Andrews introduced Durfee symbols and k-marked Durfee symbols so as to give a combinatorial interpretation for the symmetrized moment function η_2k (n) of ranks. He also considered the relations between odd Durfee symbols and the mock theta function ω(q), and proved that the 2k-th moment function η_2k^o (n) of odd ranks of odd Durfee symbols counts (k+1)-marked odd Durfee symbols of n. In this talk, we study asymptotic and monotonic properties of the odd rank function N^o (m,n). Wright's variant of the Hardy-Ramanujan circle method is employed to obtain an asymptotic formula for N^o (m,n). Besides, Combinatorial proofs are given for some inequalities on the monotonicity of N^o (m,n). We also give an asymptotic formula for the symmetrized positive odd rank moment η_k^(o+) (n) and provide a combinatorial interpretation of η_k^(o+) (n)  involving odd Durfee symbols.

报告人简介：刘勇杉，博士毕业于南开大学组合数学中心，师从著名组合数学家陈永川院士。现于重庆邮电大学工作，目前主要研究Mock Theta函数以及k-marked Durfee记号，它们的渐进性质、算术性质以及单峰性等，已有研究工作发表在Int. J. Number Theory等数论与组合方向的权威期刊上。

学院联系人:傅士硕

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