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Enumerating (Multiplex) juggling sequences. (English) Zbl 1231.05009
Summary: We consider the problem of enumerating periodic \(\sigma\)-juggling sequences of length \(n\) for multiplex juggling, where \(\sigma\) is the initial state (or 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 Chung and Graham.

MSC:
05A15 Exact enumeration problems, generating functions
00A08 Recreational mathematics
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References:
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