Juggling and applications to \(q\)-analogues (Q1924362)

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 \(\widetilde A_{d-1}\).