报告人: 唐大钊(重庆师范大学)
时间：2023年11月13日 （星期一）10:30-11:30
地点：腾讯会：754-139-165
腾讯会议链接 //meeting.tencent.com/dm/mxi3N7M6ih3J
报告摘要: In 2004, Corteel and Lovejoy introduced the notion of overpartitions in order to give a combinatorial proof of several celebrated $q$-series identities. Let $\overline{p}(n)$ denote the number of overpartitions of $n$. Many scholars have been investigated subsequently congruence properties modulo powers of $2$ satisfied by $\overline{p}(n)$. Congruence properties modulo powers of 2 for $\overline{pp}(n)$ were also considered by several scholars, where $\overline{pp}(n)$ denotes the number of overpartition pairs of $n$. In this talk, utilizing some $q$-series identities and iterative computations, we prove several internal congruences and congruences modulo powers of 2 enjoyed by $\overline{p}(n)$ and $\overline{pp}(n)$. Moreover, we conjecture that these internal congruences and congruences are initial cases in the corresponding internal congruence families and congruence families. Finally, we pose a related conjecture and some questions that merit further investigation.
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邀请人：毛仁荣