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2 cards from this section. Quick, good the night before a test.
What is the value of C(2, 1)?
Think of the number of ways to choose 1 from 2.
Define what a bad sequence is in the context of Catalan numbers.
Consider what violates the sequence of valid parenthesis.
What do Catalan numbers count?
Think about the nature of matching pairs.
The reflection method maps bad sequences to valid sequences.
Consider how reflection alters the sequences.
Devise an alternate proof for the formula for Catalan numbers without using the reflection method.
Focus on how smaller sequences of parentheses can combine to form larger ones.
Calculate C(2n, n) for n = 4 and explain how it relates to Catalan numbers.
Don't forget to apply the formula for C(2n, n) directly!
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