The multiplicities of a dual-thin Q-polynomial association scheme

Abstract

Let Y = (X, {Ri}0≤i≤D) denote a symmetric association scheme, and assume that Y is Q-polynomial with respect to an ordering E 0, ...,ED of the primitive idem-potents. Bannai and Ito conjectured that the associated sequence of multiplicities mi (0 ≤ i ≤ D) of Y is unimodal. Talking to Terwilliger, Stanton made the related conjecture that mi ≤ mi+1 and mi ≤ m D-i for i