Juggling and applications to q-analogues

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


We consider 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. Using a crossing statistic, we obtain explicit q-enumeration formulas. Our techniques give a natural combinatorial interpretation of the q-Stirling numbers of the second kind and a bijective proof of an identity of Carlitz. By generalizing these techniques, we give a bijective proof of a q-identity involving unitary compositions due to Haglund. Also, juggling patterns enable us to easily compute the Poincaré series of the affine Weyl group Ãd-1.

Original languageEnglish
Pages (from-to)107-125
Number of pages19
JournalDiscrete Mathematics
Issue number1-3
StatePublished - Oct 1 1996

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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