20.6. Conclusion and Summary

Try these first

1. 1.

   What does C(0) equal?

   Hint

   How many valid sequences are possible with no pairs?

2. 2.

   What is the value of C(1)?

   Hint

   Think of the simplest case of one pair of parentheses.

3. 3.

   What is the value of C(3)?

   • 3
   • 5
   • 7

   Hint

   Recall the example we discussed regarding valid arrangements.

4. 4.

   Is C(n) always equal to a positive integer?

   • True
   • False

   Hint

   Think about what Catalan numbers represent in combinatorics.

5. 5.

   Calculate C(4) using the recurrence relation and list all valid sequences.

   Hint

   List combinations for n = 3 and apply them step-wise.

6. 6.

   Explore another combinatorial problem that shares a bijection with Catalan numbers. Describe it.

   Hint

   Draw the connection based on how parentheses reflect balance in sequences.