题目：Some generating functions and inequalities for the Andrews--Stanley partition functions
报告人：夏先伟教授，江苏大学
时间：2020/6/19（周五）15:30-16:30
腾讯会议ID：663 520 220
摘要： Let $\mathcal {O}(\pi)$ denote the number of odd parts in an integer partition $\pi$. In 2005, Stanley introduced a new statistic $ \operatorname{srank}(\pi)=\mathcal {O}(\pi)-\mathcal {O}(\pi')$, where $\pi'$ is the conjugate of $\pi$. Let $p(r,m;n)$ denote the number of partitions of $n$ with srank congruent to $r$ modulo $m$. Generating functions, congruences and inequalities for $p(0,4;n)$ and $p(2,4;n)$ were then established by a number of mathematicians, including Stanley, Andrews, Swisher,Berkovich and Garvan. Motivated by these work, we deduce some generating functions and inequalities for $p(r,m;n)$ with $m=16$ and $24$. These results are refinements of some inequalities due to Swisher.
This is a joint work with Na Chen, Shane Chern and Yan Fan.
报告人介绍：夏先伟，男，1982年生，教授，博士生导师。2010年博士毕业于南开大学，师从陈永川教授，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., Proc. Royal Soc. Edinburgh. Section A, Pacific J. Math., European J. Combin., Acta Arithm., J. Number Theory等国外学术期刊上发表研究论文50余篇。
