Let X be a finite set and let R_i(i = 0,1,... ,d) be relations on X, i.e., subsets of X x X. X = (X, {R_i}_(0 ≤ i ≤ d )) is a commutative association scheme of d classes if the following conditions hold. (1) R_0 = {(x,x)|x∈ X}, (2) X x X = R_0 ∪ R_1 ∪ ... ∪ R_d and R_i ∩ R_j = φ if i ≠ j, (3) ~tR_i = R_(i′) for some i′ ∈ {0,1,...,d}, where ~tR_i = {(x,y)|(y,x) ∈ R_i}, (4) for i,j, k ∈ {0,1,... ,d}, the number of z ∈ X such that (x,z) ∈ R_i and (z,y) ∈ R_j is a constant p_(ij)~k whenever (x, y) ∈ R_k, (5) p_(ij)~k = p_(ji)~k for all i, j, k ∈ {0,1,...,d}. The non-negative integers p_(ij)~k are called the intersection numbers of X.
展开▼
机译：令X为有限集，令R_i（i = 0,1，...，d）为X上的关系，即X x X的子集。X =（X，{R_i} _（0≤i≤d ））是满足以下条件的d类的交换关联方案。 （1）R_0 = {（x，x）|x∈X}，（2）X x X = R_0∪R_1∪...∪R_d和R_i∩R_j =φ如果i≠j，（3）〜tR_i =对于某些i'∈{0,1，...，d}，R_（i'），其中〜tR_i = {（x，y）|（y，x）∈R_i}，（4）对于i，j， k∈{0,1，...，d}，z∈X的个数使得（x，z）∈R_i和（z，y）∈R_j为常数p_（ij）〜k y）∈R_k，（5）对于所有i，j，k∈{0,1，...，d}，p_（ij）〜k = p_（ji）〜k。非负整数p_（ij）〜k称为X的交点数。
展开▼
