A369380 Number of main classes of diagonal Latin squares containing Dabbaghian-Wu pandiagonal Latin squares of order 2n+1.

1, 0, 0, 1, 0, 0, 8, 0, 0, 18, 0, 0

Offset: 1

Author

Eduard I. Vatutin, Jan 22 2024

Keywords

• nonn
• more

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.
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A338562, A342306, A368027, A369379.