Allgemeine schnittzahlen in t-designs

AbstractLet b⊆Vk be a t −(υ, kλ)-design and M ⊆ v with t ⩽ m := |M|. Then we call for 0⩽j⩽mαj=|{B∈b|B∩M|=j}| the jth intersection number of M in b. In this paper is proved, that αj=λz.ccirf;υ − tk − t-1⋅∑r=jt(-1)rrjmrυ − rk − r ++(-1)t+kj+1⋅∑r=0m−1−tt+r−jrt+r−1jαt+r+1 holds for 0⩽j⩽m and arbitary M ⊆ V with t ⩽ m=|M|. from these equations one can derive several necessary conditions for the existence of t-designs and also non-existence theorems. Weproved here for instance the followin