Graphs and Combinatorics

, Volume 2, Issue 1, pp 101–112 | Cite as

Association schemes and quadratic transformations for orthogonal polynomials

  • Laura Chihara
  • Dennis Stanton


Special cases of the Askey-Wilson polynomials are the eigenmatrices of the classical association schemes. Three constructions on the schemes — multiple polynomial structures, bipartite halves, and antipodal quotients — give quadratic transformations for the polynomials. It is shown that these transformations essentially follow from a quadratic transformation for the Askey-Wilson polynomials. Explicit formulas for the eigenmatrices of three related association schemes are given.


Explicit Formula Orthogonal Polynomial Association Scheme Classical Association Related Association 
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Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Laura Chihara
    • 1
  • Dennis Stanton
    • 2
  1. 1.Department of MathematicsSt. Olaf CollegeNorthfieldUSA
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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