Skip to main content
Top

2015 | OriginalPaper | Chapter

Some Results on the Krein Parameters of an Association Scheme

Authors : Vasco Moço Mano, Enide Andrade Martins, Luís Almeida Vieira

Published in: Dynamics, Games and Science

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

We consider association schemes with d classes and the underlying Bose-Mesner algebra, \(\mathcal{A}\). Then, by taking into account the relationship between the Hadamard and the Kronecker products of matrices and making use of some matrix techniques over the idempotents of the unique basis of minimal orthogonal idempotents of \(\mathcal{A}\), we prove some results over the Krein parameters of an association scheme.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Bailey, R.A.: Association Schemes, Designed Experiments, Algebra and Combinatorics. Cambridge University Press, Cambridge (2004)CrossRefMATH Bailey, R.A.: Association Schemes, Designed Experiments, Algebra and Combinatorics. Cambridge University Press, Cambridge (2004)CrossRefMATH
2.
go back to reference Bose, R.C.: Strongly regular graphs, partial geometries and partially balanced designs. Pac. J. Math. 13, 389–419 (1963)CrossRefMATH Bose, R.C.: Strongly regular graphs, partial geometries and partially balanced designs. Pac. J. Math. 13, 389–419 (1963)CrossRefMATH
3.
go back to reference Bose, R.C., Mesner, D.M.: On linear associative algebras corresponding to association schemes of partially balanced designs. Ann. Math. Stat. 30, 21–38 (1959)MathSciNetCrossRefMATH Bose, R.C., Mesner, D.M.: On linear associative algebras corresponding to association schemes of partially balanced designs. Ann. Math. Stat. 30, 21–38 (1959)MathSciNetCrossRefMATH
4.
go back to reference Bose, R.C., Shimamoto, T.: Classification and analysis of partially balanced incomplete block designs with two associate classes. J. Am. Stat. Assoc. 47, 151–184 (1952)MathSciNetCrossRefMATH Bose, R.C., Shimamoto, T.: Classification and analysis of partially balanced incomplete block designs with two associate classes. J. Am. Stat. Assoc. 47, 151–184 (1952)MathSciNetCrossRefMATH
5.
6.
go back to reference Delsarte, P.: An algebraic approach to the association schemes of coding theory. Philips Res. Rep. Suppl. 10, 97 (1973)MathSciNet Delsarte, P.: An algebraic approach to the association schemes of coding theory. Philips Res. Rep. Suppl. 10, 97 (1973)MathSciNet
8.
go back to reference Higman, D.G.: Coherent configurations part I: ordinary representation theory. Geometriae 4, 1–32 (1975)MathSciNetMATH Higman, D.G.: Coherent configurations part I: ordinary representation theory. Geometriae 4, 1–32 (1975)MathSciNetMATH
10.
11.
go back to reference Horn, R., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambidge (1991)CrossRefMATH Horn, R., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambidge (1991)CrossRefMATH
12.
go back to reference Lint, J.H.V., Wilson, R.M.: A Course in Combinatorics. Cambridge University Press, Cambridge (2006) Lint, J.H.V., Wilson, R.M.: A Course in Combinatorics. Cambridge University Press, Cambridge (2006)
13.
go back to reference Scott, L.L. Jr.: A condition on Higman’s parameters. Notices Am. Math. Soc. 20 (A-97), 721-20-45 (1973) Scott, L.L. Jr.: A condition on Higman’s parameters. Notices Am. Math. Soc. 20 (A-97), 721-20-45 (1973)
14.
go back to reference Shakan, G., Xin, Y.: Q-Polynomial Association Schemes with Irrational Eigenvalues. A Major Qualifying Project submitted to the Faculty of the Worcester Polytechnic Institute (2012) Shakan, G., Xin, Y.: Q-Polynomial Association Schemes with Irrational Eigenvalues. A Major Qualifying Project submitted to the Faculty of the Worcester Polytechnic Institute (2012)
Metadata
Title
Some Results on the Krein Parameters of an Association Scheme
Authors
Vasco Moço Mano
Enide Andrade Martins
Luís Almeida Vieira
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-16118-1_23

Premium Partner