Self-Complementary Magic Squares.
Self-Complementary Magic Squares.
This paper considers magic squares on the symbols 1 to \(n^2\). The complement of such a square is obtained by replacing each symbol \(s\) by \(n^2+1-s\). Two magic squares are equivalent if one can be mapped to the other by some element of the dihedral group of order 8. A magic square is self-complementary if it is equivalent to its complement. The authors give a structural characterisation of self-complementary magic squares and a proof that they exist for all orders \(n\geq3\). The existence proof relies on earlier known results for odd \(n\).
self-complementary magic square, Orthogonal arrays, Latin squares, Room squares, magic square, Other designs, configurations, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
self-complementary magic square, Orthogonal arrays, Latin squares, Room squares, magic square, Other designs, configurations, Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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