Abstract
Using covering numbers we prove that a standard real integral table algebra (A, B) with |B| ≥ 6 has a P-polynomial structure with respect to every b ≠ 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| ≤ 5.
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Xu, B. Table algebras with multiple P-polynomial structures. J Algebr Comb 23, 377–393 (2006). https://doi.org/10.1007/s10801-006-8349-7
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DOI: https://doi.org/10.1007/s10801-006-8349-7