Problems/Erdos-Ko-Rado Theorem

Erdos-Ko-Rado Theorem

CombinatoricsSOLVED
Year
1961
Difficulty
*****
Solved by
Paul Erdos, Chao Ko & Richard Rado (1961)

Statement

Maximum size of an intersecting family of r-element subsets of an n-element set.

∣F∣≤(n−1r−1)for n≥2r|\mathcal{F}| \leq \binom{n-1}{r-1} \quad \text{for } n \geq 2r

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A cornerstone of extremal set theory with deep applications in coding theory and computer science.

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