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Chapter 7

Chapter 7. Generating Function and Applications. 7.2 Generating Function. Definition of Generating Function G(x): e.g. vs. e.g. 1.2. e.g. 1.4 =?. e.g. 2.2 (NCKU) Show that Constant term is. Considering constant term is.

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Chapter 7

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  1. Chapter 7 Generating Function and Applications

  2. 7.2 Generating Function

  3. Definition of Generating Function G(x): e.g. vs.

  4. e.g. 1.2

  5. e.g. 1.4 =?

  6. e.g. 2.2 (NCKU) Show that Constant term is

  7. Considering constant term is

  8. 7.3 Application(1): Solving Recurrence

  9. Example 1 Solve with and . From and , we have From , we have

  10. From original recurrence and boundary conditions, we further have

  11. We have Final solution is

  12. Reading Assignment: Solve nonhomogeneous recurrence By using generating function.

  13. 7.4 Application(2): Combinatorial Counting

  14. Example 4 Given n nodes, how many rooted binary trees that we can build up? When n=5, there are five trees.

  15. Recurrence: We still need the boundary conditions: , , and

  16. We have and It yields to

  17. Derivation:

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