The Erdös-Ko-Rado theorem for vector spaces

AbstractLet V be an n-dimensional vector space over GF(q) and for integers k⩾t>0 let mq(n, k, t) denote the maximum possible number of subspaces in a t-intersecting family F of k-dimensional subspaces of V, i.e., dim F ∩ F′ ⩾ t holds for all F, F′ ϵ F. It is shown that mq(n,k,t)=maxn−tk−t, 2k−tk for n⩾2k−t while for n⩽2k−t trivially mq(n,k,t)=nk holds