A note on thin P-polynomial and dual-thin Q-polynomial symmetric association schemes

Let Y denote a d-class symmetric association scheme, with d greater than or equal to 3. We skew the following: If Y admits a P-polynomial structure with intersection numbers p(ij)(h) and Y is 1-thin with respect to at least one vertex, then p(1l)(l)=0=double right arrow p(1i)(i)=0 1 less than or equal to i less than or equal to d-1 If Y admits a Q-polynomial structure with Krein parameters q(ij)(h), and Y is dual 1-thin with respect to at least one vertex,then q(1l)(l)=0 double right arrow q(1i)(i)=0 1 less than or equal to i less than or equal to d-1.