A Class ofP-polynomial Table Algebras with and without Integer Multiplicities

On the Calculation of Multiplicities forP-PolynomialC-Algebras

“…The proof generalizes the method of Bannai and Ito in their classification of Moore graphs [3, Theorem III.3.1], and to some extent their approach in [4][5][6]. The formulas derived here also have application (in particular, in a sequel to this article [9]) when g is small, even when g = 1. So we assume only that g ≥ 1. where d = m + l = n + g + l l ≥ 1 g ≥ 1 n ≥ 0 , c a b = c n a n b n , and c a b = c m+1 a m+1 b m+1 , so that the triples for g ≥ 1 consecutive columns are equal.…”

The Application of Tridiagonal Matrices in P-polynomial Table Algebras

“…In this section, we review some important concepts from table algebras and P-polynomial table algebras; see Blau and Hein (2014) and Xu (2012) for more details.…”

The Application of Tridiagonal Matrices in P-polynomial Table Algebras

“…In this section, we review some important concepts from table algebras and P-polynomial table algebras; see [4] and [13] for more details.…”

“…Tridiagonal matrices are also used in P-polynomial table algebras. More precisely, the first intersection matrix of a P-polynomial table algebra is a tridiagonal matrix whose eigenvalues can give all characters of the P-polynomial table algebra, see [4,Remark 3.1]. The study of characters of table algebras is important and can be used in studying the properties of association schemes, because the Bose-Mesner algebra of any association scheme is a table algebra, see [11].…”