2.4.4. Part (c): Stirling Function of Type 2

Try these first

1. 1.

   Define the Stirling function of type 2.

   Hint

   What does the S in S(r, s) represent?

2. 2.

   What is a surjective function?

   Hint

   Think about input-output relationships in functions.

3. 3.

   What does S(3, 2) represent?

   • Ways to divide 3 elements into 2 subsets
   • Ways to arrange 3 elements
   • Ways to assign values

   Hint

   Focus on what the Stirling function describes.

4. 4.

   Is every surjective function a bijection?

   • True
   • False

   Hint

   Think of the definitions of surjective and bijective relationships.

5. 5.

   What would S(10, 5) illustrate in the context of a classroom with 10 students needing to form 5 groups?

   Hint

   Use Stirling number properties to derive the answer.

6. 6.

   Given S(6, 2), how would you compute the number of surjective functions from a 6-element set X to a 2-element set Y?

   Hint

   Think about how multiple arrangements affect mappings.