KITE-FREE P-POLYNOMIAL AND Q-POLYNOMIAL SCHEMES

Let Y=(X,{R(i)}(0 less than or equal to i less than or equal to d)) denote a P-polynomial association scheme. By a kite of length i (2 less than or equal to i less than or equal to d) in Y, we mean a 4-tuple xyzu (x, y, z, u is an element of X) such that (x, y)is an element of R(1), (x, z)is an element of R(1), (y, z)is an element of R(1), (u,y)is an element of R(i-1), (u, z)is an element of R(i-1),(u, x)is an element of R(i). Our main result in this paper is the following.