报告人： 季青教授
报告题目：Overpartitions and Bressoud’s conjecture
报告时间：2022年1月16日（周日）下午2:00
报告地点：腾讯会议 561154794
主办单位：数学与统计学院、科学技术研究院
报告人简介：
季青，天津大学教授，2007年于南开大学获得理学博士学位，主要从事q-级数和整数分拆理论的研究，先后在Adv. Math.、J. Reine Angew. Math.、Trans. Amer. Math. Soc.、J. Combin. Theory A等期刊上发表多篇论文。先后主持国家自然科学基金项目优秀青年基金项目和面上基金项目，参与创新群体项目和重点项目。
报告摘要：
In 1980, Bressoud conjectured a combinatorial identity $A_j=B_j$ for $j=0$ or $1$, where the function $A_j$ can be viewed as the generating function of the number of partitions with certain congruence conditions and the function $B_j$ can be viewed as the generating function of the number of partitions with certain difference conditions. Bressoud's conjecture specializes to a wide variety of well-known theorems in the theory of partitions. Special cases of his conjecture have been subsequently proved by Bressoud, Andrews, Kim and Yee. Recently, Kim resolved Bressoud's conjecture for the case $j=1$.
In this talk, we introduce a new partition function $\overline{B}_j$ which can be viewed as an overpartition analogue of the partition function $B_j$ introduced by Bressoud. By means of Gordon markings, we build bijections to obtain a relationship between $\overline{B}_1$ and $B_0$ and a relationship between $\overline{B}_0$ and $B_1$. Based on these former relationships, we further give overpartition analogues of many classical partition theorems including Euler's partition theorem, the Rogers-Ramanujan-Gordon identities, the Bressoud-Ramanujan-Gordon identities, the Andrews-G\ollnitz-Gordon identities and the Bressoud-G\ollnitz-Gordon identities.