Abstract
In this paper we study the polynomiality and co-polynomiality of association schemes. These two notions were introduced by Ito. We show that P-polynomial association schemes are co-polynomial and Q-polynomial association schemes are polynomial. We also determine the polynomiality and co-polynomiality for 3-class association schemes. Further we give examples of association schemes that are polynomial but not co-polynomial, or co-polynomial but not polynomial.
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