Combinatorial Choreography

Tom Verhoeff
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 607–612 Workshop papers


Together with the workshop participants, we investigate various ways to express combinatorial structures through persons and/or physical objects in motion. For instance, the six permutations of three elements can be presented by three persons in a dance. Each person represents an element. They stand next to each other, and, five times, two appropriately selected neighbors swap places. Each swap can be artistically executed. Alternatively, the three persons can hold three physical objects to represent the three elements, and they exchange objects to present the six permutations.

This is a discovery workshop, where I will guide you through some of the combinatorial structures that I have investigated. Even simple combinatorial structures give rise to interesting mathematical questions when trying to present them through persons and physical objects. The design of a choreography can lead to surprising insights.

There will also be room to work on designing your own choreography for a combinatorial structure of your choice. Finally, we reflect on possible applications in education.