Siteswap

A siteswap is a sequence encountered in Juggling in which each term is a Positive integer, encoded in Binary. The transition rule from one term to the next consists of changing some 0 to 1, subtracting 1, and then dividing by 2, with the constraint that the Division by two must be exact. Therefore, if a term is Even, the bit to be changed must be the units bit. In siteswaps, the number of 1-bits is a constant.

Each transition is characterized by the bit position of the toggled bit (denoted here by the numeral on top of the arrow). For example,

$111 \smash{\mathop{\longrightarrow}\limits^{5}} 10011 \smash{\mathop{\longright... ...ongrightarrow}\limits^{1}} 1011 \smash{\mathop{\longrightarrow}\limits^{2}} 111$
$\smash{\mathop{\longrightarrow}\limits^{6}} 100011 \smash{\mathop{\longrightarr... ...tarrow}\limits^{0}} 111 \smash{\mathop{\longrightarrow}\limits^{4}} 1011 \ldots$

The second term is given from the first as follows: 000111 with bit 5 flipped becomes 100111, or 39. Subtract 1 to obtain 38 and divide by two to obtain 19, which is 10011.

See also Juggling

References

Juggling Information Service. ``Siteswaps.'' http://www.juggling.org/help/siteswap/.