学术报告报告题目: Card Shuffle groups
报 告 人: 夏彬绉 博士 (NR Lecturer in Graph Theory)
报告时间： 2026 年 10 月 28 日（星期三）下午 16:00-17:00
报告地点： 37 号楼（清清文理楼）3A02
邀 请 人: 周胜林 教授
欢迎广大师生前往！
数学学院
2026 年 10 月 25 日
报告摘要：
Shuffling a deck of cards is often encountered in card tricks. There are a number of questions that may be of concern, such as how a shuffle changes the order of the deck, and how many different orderings can be obtained by shuffling the deckrepeatedly. The latter question is to determine the permutation group, called the shuffle group, generated by all the consideredshuffles. More precisely, for positive integers k and n, the shuffle group $G_{k,kn}$ is generated by the k! permutations of a deck of kn cards performed by cutting the deck into k piles with n cards in each pile, and then perfectly interleaving these cardsfollowing certain order of the k piles. The shuffle group $G_{2,2n}$ was completely determined by Diaconis, Graham andKantor in 1983, and a conjectural classification has been made in the literature for the general $G_{k,kn}$. In this talk, I will report the joint work with J. Zhang, Z. Zhang and W. Zhu to confirm this conjectural classification.
报告人介绍：
夏彬绉，2009 年本科毕业于浙江大学，2014 年获得北京大学博士学位。2014-2016 年于北京国际数学研究中心从事博士后研究，2016-2017 年西澳大利亚大学 Research associate，2017 年起任职于墨尔本大学。现任澳洲与新西兰组合数学协会主席，主要研究方向为有限群论与代数图论。曾获国际组合及其应用研究所 2017 年 KirkmanMedal 和 2025 年 Hall Medal。与合作者解决多个长期公开问题，包括：完成 Wielandt 于上世纪 70 年代提出的几乎单群分解的分类问题；证明 Lovász 等人于 1982 年提出的关于几乎所有凯莱图全自同构群的猜想；解决 40 多年来悬而未决的洗牌群问题。