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Let V be a finite dimensional vector space over a finite field. A family F consisting of k-subspcaes of V is called almost t-intersecting if for each F F there is at most one F^ F with (F F^) t-1. In this paper, we determine the maximum value and the extremal structure of almost t-intersecting families. We also solve the same problems for almost t-intersecting families but not t-intersecting.
Liu et al. (Sun,) studied this question.
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