A GAP Package for Computation with Coherent Configurations

  • Dmitrii V. Pasechnik
  • Keshav Kini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)


We present a GAP package for computing with Schurian coherent configurations and their representations.


GAP coherent configuration association scheme permutation group GRAPE Sage semidefinite programming centralizer ring 


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  1. 1.
    Bannai, E., Ito, T.: Algebraic Combinatorics I: Association Schemes. Benjamin/Cummings (1984)Google Scholar
  2. 2.
    Cameron, P.J.: Permutation groups. London Mathematical Society Student Texts, vol. 45. Cambridge University Press, Cambridge (1999)zbMATHGoogle Scholar
  3. 3.
    Miyamoto, I.: Computation of isomorphisms of coherent configurations. Ars Mathematica Contemporanea 3(1) (2010)Google Scholar
  4. 4.
    Pasechnik, D., Kini, K.: Cohcfg, a GAP package for coherent configurations (preliminary version) (2010),
  5. 5.
    Schrijver, A.: New code upper bounds from the Terwilliger algebra and semidefinite programming. IEEE Trans. Inform. Theory 51(8), 2859–2866 (2005)CrossRefMathSciNetGoogle Scholar
  6. 6.
    de Klerk, E., Pasechnik, D.V., Schrijver, A.: Reduction of symmetric semidefinite programs using the regular *-representation. Math. Prog. B 109, 613–624 (2007); e-print 2005-03-1083, Optimization OnlinezbMATHCrossRefGoogle Scholar
  7. 7.
    de Klerk, E., Pasechnik, D.V., Maharry, J., Richter, B., Salazar, G.: Improved bounds for the crossing numbers of K m,n and K n. SIAM J. Discr. Math. 20, 189–202 (2006)zbMATHCrossRefGoogle Scholar
  8. 8.
    Vallentin, F.: Symmetry in semidefinite programs. Linear Algebra Appl. 430(1), 360–369 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Ivanov, A.A., Pasechnik, D.V., Seress, A., Shpectorov, S.: Majorana representations of the symmetric group of degree 4. J. of Algebra (submitted)Google Scholar
  10. 10.
    Grohe, M.: Fixed-point definability and polynomial time on graph with excluded minors. In: 25th IEEE Symposium on Logic in Computer Science, LICS 2010 (to appear 2010) Google Scholar
  11. 11.
    Weisfeiler, B. (ed.): On Construction and Identification of Graphs. LNM, vol. 558. Springer, Berlin (1976)zbMATHGoogle Scholar
  12. 12.
    The GAP Group: GAP – Groups, Algorithms, and Programming, Version 4.4.12. (2008),
  13. 13.
    Stein, W., et al.: Sage Mathematics Software (Version 4.4). The Sage Development Team (2010),
  14. 14.
    Soicher, L.H.: GRAPE: a system for computing with graphs and groups. In: Finkelstein, L., Kantor, W. (eds.) Groups and Computation. DIMACS Series in Discrete Mathematics and Theoretical CS, vol. 11, pp. 287–291. AMS, Providence (1993)Google Scholar
  15. 15.
    Faradzev, I.A., Klin, M.H.: Computer package for computations with coherent configurations. In: ISSAC 1991, Proc. Symposium on Symbolic and Algebraic Computation, pp. 219–221. Association for Computing Machinery, New York (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Dmitrii V. Pasechnik
    • 1
  • Keshav Kini
    • 1
  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore

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