Extending Shannon's Theorem to a General Juggling Pattern
Yeung Yam, Jingyan Song · Studies in Applied Mathematics · 1998
This article incorporates timing considerations into the site‐swap method and shows that the total dwell time, vacant time, and flight time over a period of a general juggling pattern satisfy the same equation as that in Shannon's original work for uniform juggle. Necessary and sufficient conditions on the dwell ratios to facilitate an executable juggling sequence are presented. The range of possible juggling periods incorporating maximum and minimum length of dwell times is also given.