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Various ways of describing juggling patterns on paper have been developed. These include siteswap notation, ladder diagrams, causal diagrams, and landing schedules. Most require some restrictive assumptions about the form of the juggling, so can only describe a subset of possible patterns. Some of the notations can be combined with mathematical theory to find, for example, the total number of patters of a certain length with a given number of balls.

Links:

Juggling Drops and Descents Complex math and applications to juggling patterns. A joint research by Joe Buhler of Reed College and Ron Graham of AT&T Bell Labs. www.cecm.sfu.ca/organics/papers/buhler

Introduction to SiteSwaps A concise introduction to the written juggling notation called SiteSwaps. www.cix.co.uk/~solipsys/new/SiteSwap.html

The Science of Juggling A paper from Scientific American, November 1995. Includes an overview of learning mechanisms, robot jugglers, and mathematical theory. www2.bc.edu/~lewbel/jugweb/science-1.html

Siteswap FAQ Provides answers to common questions about siteswap notation. www.juggling.org/help/siteswap/faq.html

Juggling Theory An introduction to siteswap notation, illustrated by animated gifs. de.geocities.com/unijmeyer/JugglingTheoryFrameset.html