Intersection theorems for (-1,0,1)-vectors

04/18/2020

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by   Peter Frankl, et al.

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In this paper, we investigate Erdős–Ko–Rado type theorems for families of vectors from {0,± 1}^n with fixed numbers of +1's and -1's. Scalar product plays the role of intersection size. In particular, we sharpen our earlier result on the largest size of a family of such vectors that avoids the smallest possible scalar product. We also obtain an exact result for the largest size of a family with no negative scalar products.