Geodesic
The multiplicities of a dual-thin \(Q\)-polynomial association scheme
The electronic journal of combinatorics, Tome 8 (2001) no. 1
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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.
DOI : 10.37236/1589
Classification : 05E30
Mots-clés : association schemes, dual-thin schemes 
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     author = {Bruce E. Sagan and John S. Caughman, IV},
     title = {The multiplicities of a dual-thin {\(Q\)-polynomial} association scheme},
     journal = {The electronic journal of combinatorics},
     year = {2001},
     volume = {8},
     number = {1},
     doi = {10.37236/1589},
     zbl = {0973.05081},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1589/}
}
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Bruce E. Sagan; John S. Caughman, IV. The multiplicities of a dual-thin \(Q\)-polynomial association scheme. The electronic journal of combinatorics, Tome 8 (2001) no. 1. doi: 10.37236/1589

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