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4 cards from this section. Quick, good the night before a test.
What is the value of C(2)?
Use the known values or compute based on the recurrence relation.
List two valid parentheses arrangements for n=1.
Consider how many pairs you can create.
What is the recurrence relation for Catalan numbers?
Think about how the sequence can be broken down.
Is C(0) equal to 1?
Consider the case with no pairs.
Provide a detailed construction of C(n) = (2n choose n)/(n + 1) utilizing the combinatorial principles of choosing elements.
Using paths, connect the elements of combinatorial counting to valid structures.
Explain how to derive C(n) through a direct combinatorial argument involving the more complex arrangements of sequences.
Think about finite sequences of up and down steps that match to openings and closings.
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