Counting the Number of Site Swap Juggling Patterns with Respect to Particular Ceilings

Mathematics – Combinatorics

Scientific paper

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10 pages, submitted to the 11-th Bridges Conference (2008) on Mathematics and art

Scientific paper

Site swap is a mathematical notation used by jugglers to communicate, create and study complex juggling patterns. Determining the number of possible site swap juggling patterns with respect to certain limiting parameters such as number of balls etc., is a problem that has been much studied and solved by many mathematicians. However, when the patterns have a throw height restriction (ceiling) the problem becomes difficult and is in general still open. In this article we derive some formulae for computing the number of possible juggling patterns with respect to certain ceiling types.

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