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 multi-variable versions of Askey-Wilson polynomials in the future study of general commutative association schemes.
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This material is based upon research supported by the National Science Foundation under grant number DMS-8703075.
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Bannai, E. (1990). Orthogonal Polynomials in Coding Theory and Algebraic Combinatorics. In: Nevai, P. (eds) Orthogonal Polynomials. NATO ASI Series, vol 294. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0501-6_2
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