2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146124We consider the problem of enumerating periodic $σ$-juggling sequences of length $n$ for multiplex juggling, where $σ$ 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.13 pages; 3 figures; to appear in Annals of CombinatoricsCombinatorics00A08; 05A15text