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数理基础与前沿研究论坛:Proofs of some conjectures of Chan-Mao-Osburn on Becks partition statistics

发布部门:理学院   发布人:胡锡奎   发布时间:2022年05月12日 12:04

报告题目Proofs of some conjectures of Chan-Mao-Osburn on Becks partition statistics

报告人:夏先伟 教授(苏州科技大学)                       

报告时间:20220513日(星期五)下午15:00–16:00

报告地点:腾讯会议平台(会议ID: 329-827-207

入会链接:https://meeting.tencent.com/dm/97UH9P1JgKaK             

报告摘要:

     Recently, George Beck introduced two partition statistics NT(m,j,n) and M_ω (m,j,n), which denote the total number of parts in the partition of n with rank congruent to m modulo j and the total number of ones in the partition of n with crank congruent to m modulo j, respectively. Andrews proved a congruence on NT(m,5,n), which was conjectured by Beck. Very recently, Chan, Mao and Osburn established a number of Andrews-Beck type congruences and posed several conjectures involving NT(m,j,n) and M_ω (m,j,n). Some of those conjectures were proved by Chern and Mao. In this paper, we confirm the remaining three conjectures of Chan-Mao-Osburn and three conjectures due to Mao. We also present two new conjectures on NT(m,j,n) and M_ω (m,j,n). This work was jointed with Jin, Liu and Mao.

报告人简介:

夏先伟,苏州科技大学数学科学学院教授,博士生导师,江苏省杰出青年基金获得者。2010年博士毕业于南开大学,师从陈永川院士,主要研究组合数学、特殊函数与整数分拆,在包括Math. Comput., Proc. Edinb. Math. Soc., Adv. Appl. Math., Pacific J. Math., European J. Combin., Acta Arith., J. Number Theory等期刊上发表论文多篇。主持两项国家自然科学基金面上项目

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重庆邮电大学高等研究院

                                                                              2022.05.10