The Multiplicities of a Dual-thin $Q$-polynomial Association Scheme
Keyword(s):
Let $Y=(X, \{ R_i \}_{1\le i\le D})$ denote a symmetric association scheme, and assume that $Y$ is $Q$-polynomial with respect to an ordering $E_0,...,E_D$ of the primitive idempotents. Bannai and Ito conjectured that the associated sequence of multiplicities $m_i$ $(0 \leq i \leq D)$ of $Y$ is unimodal. Talking to Terwilliger, Stanton made the related conjecture that $m_i \leq m_{i+1}$ and $m_i \leq m_{D-i}$ for $i < D/2$. We prove that if $Y$ is dual-thin in the sense of Terwilliger, then the Stanton conjecture is true.
2005 ◽
Vol 292
(1-3)
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pp. 17-44
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Keyword(s):
2000 ◽
Vol 191
(4)
◽
pp. 543-565
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1998 ◽
Vol 50
(1)
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pp. 43-56
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