Linked partition ideals and Schur's 1926 partition theorem

主讲人：陈小航, Dalhousie University

时间：2021年12月7日9：30

地点：腾讯会议 968 633 378

举办单位：数理学院

主讲人介绍：陈小航, 现为Dalhousie University 博士后, 导师为Karl Dilcher 教授。博士毕业于Pennsylvania State  University,师从美国科学院院士George Andrews教授。主要从事数论、组合数学以及特殊函数的研究，迄今在《Journal of  Combinatorial Theory, Series A》、《Journal of Number Theory》、《Discrete  Mathematics》、《Ramanujan Journal》、《Acta Arithmetica》等国际重要期刊发表学术论文多篇，并在Combinatory  Analysis 2018、Analytic and Combinatorial Number Theory: The Legacy of  Ramanujan等国际会议以及美国数学学会Joint Mathematics Meetings和Sectional Meetings上作报告。

内容介绍：Issai Schur's famous 1926 partition theorem states that the number of partitions  of $n$ into distinct parts congruent to $\pm 1$ modulo $3$ is the same as the  number of partitions of $n$ such that every two consecutive parts have  difference at least $3$ and that no two consecutive multiples of $3$ occur as  parts. In this talk, we consider some variants of Schur's theorem, especially  their Andrews--Gordon type generating functions, from the perspective of span  one linked partition ideals introduced by George Andrews. Our investigation has  interesting connections with basic hypergeometric series, $q$-difference  equations, computer algebra, and so on.