A Note on Thin P-Polynomial and Dual-Thin Q-PolynomialSymmetric Association Schemes

Abstract

Let Y denote a d-class symmetric association scheme, with d ≥ 3. We show the following: If Y admits a P-polynomial structure with intersection numbers p hij and Y is 1-thin with respect to at least one vertex, then p lll =0 → p ili =0 1 ≤ i ≤ - 1. If Y admits a Q-polynomial structure with Krein parameters q hij , and Y is dual 1-thin with respect to at least one vertex, then q lll = 0 → q ili = 01 ≤ i ≤ d-1.