Abstract
We derive a combinatorial equilibrium for bounded juggling patterns with a random, q-geometric throw distribution. The dynamics are analyzed via rook placements on staircase Ferrers boards, which leads to a stationary distribution containing q-rook polynomial coefficients and q-Stirling numbers of the second kind. We show that the stationary probabilities of the bounded model can be uniformly approximated with the stationary probabilities of a corresponding unbounded model. This observation leads to new limit formulae for q-analogues.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
