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Results in Mathematics

, Volume 44, Issue 1–2, pp 25–28 | Cite as

Semi pandiagonal magic 4 × 4-squares

  • Saleem Al-ashhab
  • Wolfgang Müller
Article
  • 45 Downloads

Abstract

It is proved that the set of all semi pandiagonal 4 × 4-squares precisely consists of 3456 squares belonging to three orbits under the faithful action of a group of order 1152 which is a semi direct product of symmetric groups.

Subject Classification

05B15 

Keywords

pandiagonal magic square group action wreath product 

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References

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    Fitting, F.: Rein mathematische Behandlung des Problems der magischen Quadrate von 16 und 64 Feldern. Jahresber. der Dt. Math. Ver. 40, 177–199 (1931)Google Scholar
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    Lehmer, D.: A Complete Census of 4 × 4-Magic Squares. Bull. Amer. Math. Soc. 39, 764–767 (1933)MathSciNetCrossRefGoogle Scholar
  3. [3]
    Müller, W.: Magische Quadrate. Math. Semesterber. 44, 131–137 (1997)MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Müller, W.: Group Actions on Magic Squares. Séminaire Lotharingien de Combinatoire S39b, 14pp. (1997)Google Scholar
  5. [5]
    Rosser, B., Walker, J.: On the Transformation Group for Diabolic Magic Squares of Order Four. Bull. Amer. Math. Soc. 44, 416–420 (1938)MathSciNetCrossRefGoogle Scholar

Copyright information

© Birkhäuser Verlag, Basel 2003

Authors and Affiliations

  1. 1.Department of MathematicsAl al-bayt UniversityMafraqJordan
  2. 2.Mathematisches InstitutUniversität BayreuthBayreuthGermany

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