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2026-03-29 14:55:31.1774796131
Bijection for Catalan Number
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HINT: Start at any vertex and go around the circle clockwise. Write down a left parenthesis,
(, the first time you come to an endpoint of a chord, and a right parenthesis,), when you come to the other endpoint. Starting at the leftmost vertex of your first picture, for instance, you’d write the sequence(())(). Show that this gives you a bijection with the set of valid strings of $n$ pairs of parentheses.