We discuss a notion of shuffle for trees which extends the
usual notion of a shuffle for two natural numbers. We give several
equivalent descriptions, and prove some algebraic and combinatorial
properties. In addition, we characterize shuffles in terms of open sets
in a topological space associated to a pair of trees. Our notion of
shuffle is motivated by the theory of operads and occurs in the theory of
dendroidal sets, but our presentation is independent and entirely selfcontained
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