A mathematical model for juggling has previously been described by Buhler, Eisenbud, Graham and Wright. This paper uses this model and observes that juggling patterns have different `states' at different times. States can be represented by polynomials. This representation is exploited to give a new proof of an enumeration theorem on juggling patterns by Buhler et al. The paper concludes by discussing state graphs and a generalization of the juggling model. Both lead to new enumeration problems.
|Permutations, words, matrices (msc 05A05), Factorials, binomial coefficients, combinatorial functions (msc 05A10), Exact enumeration problems, generating functions (msc 05A15), Paths and cycles (msc 05C38), Bell and Stirling numbers (msc 11B73)|
|CWI. Probability, Networks and Algorithms [PNA]|
Kamstra, L. (2001). Juggling polynomials. CWI. Probability, Networks and Algorithms [PNA]. CWI.