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A369380
Number of main classes of diagonal Latin squares containing Dabbaghian-Wu pandiagonal Latin squares of order 2n+1.
2
1, 0, 0, 1, 0, 0, 8, 0, 0, 18, 0, 0
OFFSET
1,7
COMMENTS
A pandiagonal Latin square is a Latin square in which the diagonal, antidiagonal and all broken diagonals and antidiagonals are transversals.
A Dabbaghian-Wu pandiagonal Latin square (see A368027) is a special type of pandiagonal Latin square (see A342306). Such squares are constructed from cyclic diagonal Latin squares (see A338562) for prime orders n=6k+1 (see Dabbaghian and Wu article) using a polynomial algorithm based on permutation of some values in Latin square. For other orders (25, 35, 49, ...) this algorithm also ensures correct pandiagonal Latin squares.
LINKS
Vahid Dabbaghian and Tiankuang Wu, Constructing non-cyclic pandiagonal Latin squares of prime orders, Journal of Discrete Algorithms, Vol. 30, 2015, pp. 70-77, doi: 10.1016/j.jda.2014.12.001.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Eduard I. Vatutin, Jan 22 2024
STATUS
approved