The Multiplicities of a Dual-thin Q-polynomial Association Scheme
Abstract
Let Y denote a symmetric association scheme which is Q-polynomial with respect to an ordering E0,...,ED of the primitive idempotents. Bannai and Ito conjectured that the associated sequence of multiplicities m0,...,mD is unimodal. We prove that if Y is dual-thin in the sense of Terwilliger, then the sequence of multiplicities satisfies mi <= mi+1 and mi <= mD-i for i < D/2.
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