Wilson's general theorem;
pairwise balanced design;
PBD-closed;
D O I:
10.1007/BF02876038
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
Given any set K of positive integers and positive integer lambda, let c(K,lambda) denote the smallest integer such that v is an element of B(K,lambda) for every integer v greater than or equal to c(K,lambda) that satisfies the congruences lambda v(v-1)=0 (mod beta(K)) and lambda(v-1)=0 (mod alpha(K)). Let K-0 be an equivalent set of K, k and k* be the smallest and the largest integers in K-0. We prove that c(K,lambda) less than or equal to exp exp{Q(0)} where [GRAPHICS] p(K-0) = Pi(l is an element of K0) l and y = k* + k(k-1) + 1.