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Enumerating (Multiplex) Juggling Sequences
Steve Butler1 and Ron Graham2
1Department of Mathematics, University of California, Los Angeles, CA 90095, USA
2Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA
Annals of Combinatorics 13 (4) pp.413-424 December, 2009
AMS Subject Classification: 00A08; 05A15
We consider the problem of enumerating periodic s-juggling sequences of length n for multiplex juggling, where s is the initial state (or landing schedule) of the balls. We first show that this roblem 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.
Keywords: juggling, multiplex, state diagram, recursions


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