文摘
Let K={k1,k2,…,kr} and L={l1,l2,…,ls} be subsets of {0,1,…,p−1} such that K∩L=0/, where p is a prime. Let be a family of subsets of [n]={1,2,…,n} with Fi () K for all and Fi∩Fj () L for any i≠j. Every subset Fi of [n] can be represented by a binary code such that aj=1 if jFi and aj=0 if jFi. Alonx2013;Babaix2013;Suzuki proved in non-modular version that if ki≥s−r+1 for all i, then . We generalize it in modular version. Alonx2013;Babaix2013;Suzuki also proved that the above bound still holds under r(s−r+1)≤p−1 and in modular version. Alonx2013;Babaix2013;Suzuki made a conjecture that if they drop one condition r(s−r+1)≤p−1 among r(s−r+1)≤p−1 and , then the above bound holds. But we prove the same bound under dropping the opposite condition . So we prove the same bound under only condition r(s−r+1)≤p−1. This is a generalization of Franklx2013;Wilson theorem (Frankl and Wilson, 1981 [2]).