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Advanced Combinatorics & Olympiad Prep
·
Module 3
The Pigeonhole Principle
1
The Pigeonhole Principle: An Introduction
State the Pigeonhole Principle (PHP) and apply it to simple distribution problems.
2
Generalized Pigeonhole Principle Applications
Apply the generalized Pigeonhole Principle to guarantee quantitative properties in distributions.
3
Proving Subset Sum/Difference Properties with PHP
Use the PHP in number-theoretic contexts to prove the existence of subsets with specific sum or difference properties.
4
The Erdős-Szekeres Theorem
Prove the Erdős-Szekeres theorem on the existence of monotonic subsequences.
Previous module
Core Counting Principles and Bijections
Next module
The Principle of Inclusion-Exclusion