Combinatorics Topics

1. Sets, Set Operations, and some Important Functions

2. Permutations and Combinations

3. Pascal's Triangle and The Binomial Theorem

4. Combinations from Multisets, The Trinomial Theorem and The Multinomial Theorem

5. Chains, Antichains, the Inclusion-Exclusion Principle, and Derangements

6. Algorithms for Generating Permutations and Combinations

7. Relations on Sets and Partial/Total Orders

8. Generating Functions and Systems of Distinct Representatives

9. Recurrence Relations

10. Special Counting Sequences and the Calculus of Finite Differences

11. Designs

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  • 1. Discrete and Combinatorial Mathematics (5th Edition) by Ralph P. Grimaldi.
  • 2. Combinatorial Designs: Constructions and Analysis by Douglas R. Stinson.
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