Erdős-Ko-Rado theorem for {0,±1}-vectors

The main object of this paper is to determine the maximum number of {0,±1}-vectors subject to the following condition. All vectors have length n, exactly k of the coordinates are +1 and one is −1, n≥2k. Moreover, there are no two vectors whose scalar product equals the possible minimum, −2. Thus, this problem may be seen as an extension of the classical Erdős-Ko-Rado theorem. Rather surprisingly there is a phase transition in the behaviour of the maximum at n=k2. Nevertheless, our solution is complete. The main tools are from extremal set theory and some of them might be of independent interest.