From organizing books to shuffling cards

The Research Cluster invites all members of its community—researchers, Professors, doctoral students, postdoctoral researchers, and research assistants—to come learn about the activities of its laboratories and platforms, and to discuss research, innovation, and technology transfer.

Imagine books on a shelf. If we wanted to sort them (by size, for example) by swapping the books in the wrong order, how many steps would it take?

Let’s change the setting: head to the casino. The dealer opens a new deck of cards and needs to shuffle them. After how many different shuffles can he be sure the deck is “properly” shuffled?

These two problems, which seem quite different at first glance, are connected to the same mathematical object: the permutohedron, obtained by cutting off the corners of a cube. After introducing these two problems, I will present the permutohedron and its connections to shuffling products and bubble sort.

This event is part of the MIPS Cluster’s monthly seminar series, which aims to foster scientific exchange and highlight new research topics and technological innovations.

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