Maths of Juggling: Minimal juggling patterns and rook placements

Minimal juggling patterns are ones where all throws are less than the period. By changing throws by multiples of n we can always get to a minimal juggling pattern (so these form a basic building block we can work with). We show that these can be associated with the ways to place non-attacking rooks on a board, so that there are n! such patterns. We also give an easy way to determine the number of balls for a minimal juggling pattern.

[eixenful]

As a juggler that use siteswaps daily, I found this really cool! You present siteswaps in such a unique way that I've never seen before! I haven't heard about the minimal juggling pattern term before. That was nice! One thing that is possible though, is to instead of subtracting the period, subtract 1 from every throw. Which also makes a new trick just with one less ball. For exmple 2312 could become 1201!

Keep making these once! Really neat!

[quidprobro]

The beard has regained its epic status! Thank you for the presentation, very informative.

[godfreypigott]

When you reduce say 741 to 111, haven't you technically turned a period-3 cycle into a period-1 cycle?