Abstract
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.
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