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Advanced Combinatorics & Olympiad Prep
·
Module 4
The Principle of Inclusion-Exclusion
1
The Principle of Inclusion-Exclusion: Formulation and Proof
Formulate and prove the general Principle of Inclusion-Exclusion (PIE).
2
Stars and Bars with Constraints
Solve complex distribution problems using the stars and bars method with upper or lower constraints.
3
Derangements and the Principle of Inclusion-Exclusion
Apply PIE to compute the number of derangements (permutations with no fixed points).
4
Surjective Functions and PIE
Apply PIE to find the number of surjective functions between two finite sets.
5
Stirling Numbers of the Second Kind: Set Partitions
Compute Stirling numbers of the second kind to solve set partition problems.
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The Pigeonhole Principle
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Invariants, Monovariants, and Coloring