Strongly symmetric self-orthogonal diagonal Latin squares and Yang Hui type magic squares

Keywords: Self-orthogonal Latin square Strongly symmetric Magic square Yang Hui type a b s t r a c t In this paper, a strongly symmetric self-orthogonal diagonal Latin square of order n with a special property (* SSSODLS(n)) is introduced. It is proved that a * SSSODLS(n) exists if and only if n ≡ 0 (mod 4) and n ̸ = 4. As an application, it is shown that there exists a Yang Hui type magic square YMS(n, 4) if and only if n ≡ 0 (mod 4) and n ̸ = 4.