Counting Prime Juggling Patterns

  title={Counting Prime Juggling Patterns},
  author={Esther Banaian and S. Butler and C. Cox and J. Davis and Jacob Landgraf and S. Ponce},
  journal={Graphs and Combinatorics},
  • Esther Banaian, S. Butler, +3 authors S. Ponce
  • Published 2016
  • Mathematics, Computer Science
  • Graphs and Combinatorics
  • Juggling patterns can be described by a closed walk in a (directed) state graph, where each vertex (or state) is a landing pattern for the balls and directed edges connect states that can occur consecutively. The number of such patterns of length n is well known, but a long-standing problem is to count the number of prime juggling patterns (those juggling patterns corresponding to cycles in the state graph). For the case of $$b=2$$b=2 balls we give an expression for the number of prime juggling… CONTINUE READING
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