计算与应用讨论班——Card Shuffle groups

报告人：夏彬㑇教授（墨尔本大学）

时间: 2024年3月28日（周四）上午10:00-12:00

地点：海纳苑2幢202

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 deck repeatedly. The latter question is to determine the permutation group, called the shuffle group, generated by all the considered shuffles. 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 cards following certain order of the k piles. The shuffle group G_{2,2n} was completely determined by Diaconis, Graham and Kantor 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 Junyang Zhang, Zhishuo Zhang and Wenying Zhu to confirm this conjectural classification.

联系人：冯涛 (tfeng@zju.edu.cn)