For sufficiently large n, an intersection-weighted sum over any k-uniform family is at most 1, with equality if and only if the family is a star.
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An Intersection-Weighted Erd\H{o}s-Ko-Rado Theorem
For sufficiently large n, an intersection-weighted sum over any k-uniform family is at most 1, with equality if and only if the family is a star.
- Local Tur\'an inequalities for walks and the spectral radius