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.