20.4.2. Bijection Between Problems

Try these first

1. 1.

   Define Catalan numbers.

   Hint

   Think about their relation to combinatorial structures.

2. 2.

   What is a valid parentheses sequence?

   Hint

   Consider the structure of parentheses in expressions.

3. 3.

   What do Catalan numbers count?

   • A. Types of graphs
   • B. Valid parentheses sequences
   • C. Network structures

   Hint

   Think about their definition.

4. 4.

   True or False: A bijection implies that two sets have the same number of elements.

   • True
   • False

   Hint

   Recall the definition of bijection.

5. 5.

   Given n = 4, compute C(4) using the recurrence relation.

   Hint

   Break down C(4) into smaller parts using known values.

6. 6.

   Design a valid parentheses sequence for n = 3, illustrating with diagrams.

   Hint

   Draw trees representations of how each sequence relates.