Graphs and Combinatorics

, Volume 2, Issue 1, pp 101–112

Association schemes and quadratic transformations for orthogonal polynomials

  • Laura Chihara
  • Dennis Stanton
Article

DOI: 10.1007/BF01788084

Cite this article as:
Chihara, L. & Stanton, D. Graphs and Combinatorics (1986) 2: 101. doi:10.1007/BF01788084

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations