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8 pages

Combinatorics

The Four Color Theorem and the Computer Mathematics Revolution: A Century-Old Enigma and the Philosophy of Mechanical Proof

The Four Color Theorem and the Computer Mathematics Revolution: A Century-Old Enigma and the Philosophy of Mechanical Proof

Inclusion-Exclusion Principle: A Powerful Technique for Correctly Counting Elements in Overlapping Sets

Inclusion-Exclusion Principle: A Powerful Technique for Correctly Counting Elements in Overlapping Sets

Permutations, Combinations, and the Binomial Theorem: The Beautiful Regularity of Numbers Seen in Pascal's Triangle

Permutations, Combinations, and the Binomial Theorem: The Beautiful Regularity of Numbers Seen in Pascal's Triangle

Burnside's Lemma: How to Count Patterns When Rotations Matter?

Burnside's Lemma: How to Count Patterns When Rotations Matter?

Catalan Numbers: Why Parentheses and Tree Structures Yield the Same Counts

Catalan Numbers: Why Parentheses and Tree Structures Yield the Same Counts

Generating Functions: What's the Benefit of Turning a Sequence into a Function?

Generating Functions: What's the Benefit of Turning a Sequence into a Function?

Sperner's Lemma: From Coloring Triangles to Existence Proofs

Sperner's Lemma: From Coloring Triangles to Existence Proofs

Ramsey Theory: Order Inevitably Emerges from Disorder — Proving Six-Person Relationships with Two Colors

Ramsey Theory: Order Inevitably Emerges from Disorder — Proving Six-Person Relationships with Two Colors