*(English)*Zbl 0704.42025

[For the entire collection see Zbl 0694.00015.]

Authorâ€™s abstract: This paper surveys the role of orthogonal polynomials in Algebraic Combinatorics, an area which includes association schemes, coding theory, design theory, various theories of group representation, and so on. The main topics discussed in this paper include the following: The connection between orthogonal polynomials and P-polynomial (or Q- polynomial) association schemes. The classification problem for P- and Q- polynomial association schemes and its connection with Askey-Wilson orthogonal polynomials, Delsarte theory of codes and designs in association schemes. The nonexistence of perfect e-codes and tight t- designs through the study of the zeros of orthogonal polynomials. The possible importance of multivariable versions of Askey-Wilson polynomials in the future study of general commutative association schemes.

##### MSC:

42C05 | General theory of orthogonal functions and polynomials |

94C30 | Applications of design theory to circuits and networks |

05C99 | Graph theory |