Juggling polynomials

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.