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Juggling and applications to \(q\)-analogues. (English) Zbl 0859.05010
The paper enumerates periodic juggling patterns where the juggler can only catch and throw one ball at a time and patterns where the juggler can handle many balls at the same time. Assigning weights to the patterns by a crossing statistic, \(q\)-enumeration results are obtained. This technique yields a natural combinatorial interpretation for the \(q\)-Stirling numbers. Juggling patterns help in computing the Poincaré series of the affine Weyl group \(\widetilde A_{d-1}\).

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