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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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