TITLE:
Association Schemes with Multiple Q-polynomial Structures


ABSTARACT:

It is well known that an association scheme X = (X,{Ri}i = 0,...,d) with k1 > 2 has at most two P-polynomial structures. The parametrical condition for an association scheme to have two P-polynomial structures is also known. In this paper, we give a similar result for Q-polynomial association schemes. In fact, if d>5, then we obtain exactly the same parametrical conditions for the dual intersection numbers or Krein parameters.

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