Geodesic
Table algebras with multiple P-polynomial structures
Journal of Algebraic Combinatorics, Tome 23 (2006) no. 4, pp. 377-393.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Using covering numbers we prove that a standard real integral table algebra (A, B) with | B| $\geq 6$ has a P-polynomial structure with respect to every $b \neq 1$ in B if and only if 2| B|-1 is prime and $( A, B)$ is exactly isomorphic to the Bose-Mesner algebra of the association scheme of the ordinary (2| B|-1)-gon. Then we present an example showing that this result is not true if | B| $\leq 5$.
Keywords: keywords table algebras, covering numbers, association schemes, Bose-mesner algebras, P-polynomial structures 
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     author = {Xu, Bangteng},
     title = {Table algebras with multiple {P-polynomial} structures},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2006__23_4_a1/}
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Xu, Bangteng. Table algebras with multiple P-polynomial structures. Journal of Algebraic Combinatorics, Tome 23 (2006) no. 4, pp. 377-393. http://geodesic.mathdoc.fr/item/JAC_2006__23_4_a1/