Enumerating (multiplex) juggling sequences

Details Enumerating (multiplex) juggling sequences Enumerating (multiplex) juggling sequences

2008-01-17

arxiv.org/abs/0801.2597v1

Mathematics

Combinatorics

13 pages; 3 figures; to appear in Annals of Combinatorics

Scientific paper

We consider the problem of enumerating periodic $\sigma$-juggling sequences of length $n$ for multiplex juggling, where $\sigma$ is the initial state (or {\em landing schedule}) of the balls. We first show that this problem is equivalent to choosing 1's in a specified matrix to guarantee certain column and row sums, and then using this matrix, derive a recursion. This work is a generalization of earlier work of Fan Chung and Ron Graham.

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