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The Catalan numbers count: • the ways a polygon with ... sides can be cut into ... triangles; • the ways to parenthesize a sequence of ... factors to be multiplied, two at a time; • the planted trivalent trees with ... leaves. This Demonstration shows the equivalence of the three interpretations by optionally labeling each polygon triangulation with the corresponding parenthesized expression, tree, or both.

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      EUN,LOM,LRE4,work-cmr-id:397776,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/EquivalenceOfThreeCatalanNumberInterpretations/,ilox,learning resource exchange,LRE metadata application profile,LRE

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