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2 cards from this section. Quick, good the night before a test.
Define Catalan numbers.
Refer to their applications in counting.
What is an injective mapping?
Think about the uniqueness of outputs.
What is the first Catalan number?
Think of the simplest valid pairing.
True or False: An injective mapping can map two distinct elements to the same element.
Recall the definition of injective functions.
Prove that the reflection method applies to sequences of parentheses and yields a unique transformation.
Reflect on the rules governing the critical points in the sequences.
Apply the concepts learned to derive the Catalan number for n = 3 and explain your steps.
Utilize both the binomial coefficients and their relationships.
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