Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric juggling with q-analogues   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 steady-state
distribution containing $q$-rook polynomial coefficients and $q$-Stirling
numbers of the second kind. We show that the equilibrium probabilities of the
bounded model can be uniformly approximated with the equilibrium probabilities
of a corresponding unbounded model. This observation leads to new limit
formulae for $q$-analogues.
  Keywords: juggling pattern; $q$-Stirling number of the second kind; Ferrers
board; Markov process; combinatorial equilibrium

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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con