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Primitive juggling sequences. (English) Zbl 1170.05006
Over the past two decades, a number of ways have been developed for representing periodic juggling patterns by finite sequences of nonnegative integers. In the most common of these, the entries of the sequence indicate how long the thrown object stays in the air. These juggling sequences have many interesting mathematical properties. In particular, each juggling sequence has associated with it a binary vector called its state. In this paper, the authors analyze the juggling sequences associated with an arbitrary state, and show how to enumerate the number of such sequences which have a given length.

MSC:
05A15 Exact enumeration problems, generating functions
05A30 \(q\)-calculus and related topics
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