Table algebras with multiple P-polynomial structures
Bangteng Xu
Eastern Kentucky University Department of Mathematics and Statistics Richmond KY 40475 Richmond KY 40475
DOI: 10.1007/s10801-006-8349-7
Abstract
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.
Pages: 377–393
Keywords: keywords table algebras; covering numbers; association schemes; Bose-mesner algebras; P-polynomial structures
Full Text: PDF
References
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7. B. Xu, Polynomial table algebras and their covering numbers, J. Algebra 176 (1995), 504-527.