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Askey-Wilson polynomials, kernel polynomials and association schemes

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Abstract

The eigenvalues of the classical association schemes are given by certain Askey-Wilson polynomials (or limiting cases). Kernel polynomials of the Askey-Wilson polynomials are also Askey-Wilson polynomials. We determine when both the Askey-Wilson polynomials and their kernels are the eigenvalues for known association schemes.

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References

  1. Askey, R., Wilson, J.: A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols. SIAM J. Math. Anal.10, I008–1016 (1979)

    Article  MathSciNet  Google Scholar 

  2. Bannai, E., Ito, T.: Algebraic Combinatorics I: Benjamin-Cummings, Menlo Park, Calif., 1984

  3. Brouwer, A.E., Cohen, A.M., Neumaier, A.: Distance regular graphs: Springer, Heidelberg, 1989

    MATH  Google Scholar 

  4. Chihara, L.: On the zeros of the Askey-Wilson polynomials with applications to coding theory. SIAM J. Anal.18, 191–207(1987)

    Article  MATH  MathSciNet  Google Scholar 

  5. Chihara, L., Stanton, D.: Association schemes and quadratic transformations for orthogonal polynomials. Graphs and Comb.2, 101-I12 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Chihara, T.S.: An Introduction to orthogonal polynomials: Gordon Breach, New York, 1978

    MATH  Google Scholar 

  7. Delsarte, P.: Properties and applications of the recurrence F(i + l,k + 1,n + 1) = qk+1F(i,k + 1,n) - qkF(i,k,n). SIAM J. Appl. Math.31, 262–270(1976)

    Article  MATH  MathSciNet  Google Scholar 

  8. Geronimus, J.: On polynomials orthogonal with respect to a given sequence of numbers and a theorem of W. Hahn. Isvestia Acad. Sc., USSR4, 215–228 (1940)

    MathSciNet  Google Scholar 

  9. Ivanov, A.A., Muzichuk, M.E., Ustimenko, V.A.: On a new family of (P andQ)-potynomial association schemes. Europ. J. Comb.10, 337-:345, (1989)

    MATH  MathSciNet  Google Scholar 

  10. Leonard, D.: Orthogonal polynomials, duality, and association schemes. SIAM J. Math. Anal.13, 656–663 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  11. Szegö, G.: Orthogonal Polynomials, Colloq Pub., vol. 23, Amer. Math. Soc., Providence R.I., 1975

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  1. Department of Mathematics, Saint Olaf College, 55057, Northfield, MN, USA

    Laura M. Chihara

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  1. Laura M. Chihara
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Chihara, L.M. Askey-Wilson polynomials, kernel polynomials and association schemes. Graphs and Combinatorics 9, 213–223 (1993). https://doi.org/10.1007/BF02988310

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  • DOI: https://doi.org/10.1007/BF02988310

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