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2 cards from this section. Quick, good the night before a test.
What does C(0) equal?
How many valid sequences are possible with no pairs?
What is the value of C(1)?
Think of the simplest case of one pair of parentheses.
What is the value of C(3)?
Recall the example we discussed regarding valid arrangements.
Is C(n) always equal to a positive integer?
Think about what Catalan numbers represent in combinatorics.
Calculate C(4) using the recurrence relation and list all valid sequences.
List combinations for n = 3 and apply them step-wise.
Explore another combinatorial problem that shares a bijection with Catalan numbers. Describe it.
Draw the connection based on how parentheses reflect balance in sequences.
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