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A Generalization of the Krein Parameters of a Symmetric Association Scheme

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Book cover Innovations in Industrial Engineering (icieng 2021)

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Abstract

In this paper we formulate a generalization of the Krein parameters of a symmetric association scheme which, in turn, allows us to deduce some necessary conditions for the existence of these schemes. This is achieved by applying some matrix analysis results over the elements of the unique basis of minimal orthogonal idempotents of the underlying algebra of a symmetric association scheme.

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References

  1. Mano, V., Vieira, L.: Symmetric association schemes and generalized Krein parameters. Int. J. Math. Models Methods Appl. Sci. 9, 310–314 (2015)

    Google Scholar 

  2. Mano, V.M., Martins, E.A., Vieira, L.A.: Some results on the Krein parameters of an association scheme. In: Bourguignon, J.P., Jeltsch, R., Pinto, A., Viana, M. (eds.) Dynamics, Games and Science. CIM Series in Mathematical Sciencess, vol. 1, Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16118-1_23

  3. Bose, R.C., Shimamoto, T.: Classification and analysis of partially balanced incomplete block designs with two associate classes. J. Am. Statist. Assoc. 47, 151–184 (1952)

    Article  MathSciNet  Google Scholar 

  4. Bose, R.C.: Strongly regular graphs, partial geometries and partially balanced designs. Pacific J. Math 13, 389–419 (1963)

    Article  MathSciNet  Google Scholar 

  5. Bose, R.C., Mesner, D.M.: On linear associative algebras corresponding to association schemes of partially balanced designs. Ann. Math. Statist. 30, 21–38 (1959)

    Article  MathSciNet  Google Scholar 

  6. Delsarte, P.: An algebraic approach to the association schemes of coding theory. Philips Research Reports Supplements 10 (1973)

    Google Scholar 

  7. Higman, D.G.: Coherent configurations part I: ordinary representation theory. Geometriae 4, 1–32 (1975)

    MathSciNet  MATH  Google Scholar 

  8. Higman, D.G.: Coherent configurations part II: weights. Geometriae 5, 413–424 (1976)

    MathSciNet  MATH  Google Scholar 

  9. Hanaki, A.: Character of association schemes and normal closed subsets. Graphs Combin. 19(3), 363–369 (2003)

    Article  MathSciNet  Google Scholar 

  10. Graham, R.L., Grötschel, M., Lovász, L. (eds.): Handbook of Combinatorics, vol. 1. The MIT Press, North-Holland, Cambridge (1995)

    MATH  Google Scholar 

  11. Horn, R., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)

    Book  Google Scholar 

  12. Horn, R., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991)

    Book  Google Scholar 

  13. Scott Jr., L.L.: A condition on Higman’s parameters. Notices Am. Math. Soc. 20, A-97, 721-20-45 (1973)

    Google Scholar 

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Acknowledgments

In this work Luís Vieira was partially supported by the Center of Research of Mathematics of University of Porto (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the program FEDER, under the partnership agreement PT2020.

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Authors and Affiliations

  1. University of Porto, Porto, Portugal

    Vasco Moço Mano

  2. University of Porto, Faculty of Engineering, Porto, Portugal

    Luís Almeida Vieira

Authors
  1. Vasco Moço Mano
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  2. Luís Almeida Vieira
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Corresponding author

Correspondence to Luís Almeida Vieira .

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Editors and Affiliations

  1. Department of Mechanical Engineering, University of Minho, Guimarães, Portugal

    José Machado

  2. Department of Industrial Electronics, University of Minho, Guimarães, Portugal

    Filomena Soares

  3. Poznan University of Technology, Poznan, Poland

    Justyna Trojanowska

  4. Department of Manufacturing Engineering, Machines and Tools, Sumy State University, Sumy, Ukraine

    Vitalii Ivanov

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Mano, V.M., Vieira, L.A. (2022). A Generalization of the Krein Parameters of a Symmetric Association Scheme. In: Machado, J., Soares, F., Trojanowska, J., Ivanov, V. (eds) Innovations in Industrial Engineering. icieng 2021. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-78170-5_39

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  • DOI: https://doi.org/10.1007/978-3-030-78170-5_39

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-78169-9

  • Online ISBN: 978-3-030-78170-5

  • eBook Packages: EngineeringEngineering (R0)

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