A360220 Maximum number of diagonal transversals in an orthogonal diagonal Latin square of order n.

1, 0, 0, 4, 5, 0, 27, 120, 333

Offset

1,4

Comments

An orthogonal diagonal Latin square is a diagonal Latin square that has at least one orthogonal diagonal mate.

a(10) >= 866, a(11) >= 4828, a(12) >= 30192, a(13) >= 131106, a(17) >= 204995269, a(19) >= 11254190082.

For most orders n, at least one diagonal Latin square with the maximal number of diagonal transversals has an orthogonal mate and A287648(n) = a(n). Known exceptions: n=6 and n=10. - Eduard I. Vatutin, Feb 17 2023

Every orthogonal diagonal Latin square is a diagonal Latin square, so A287647(n) <= A354068(n) <= a(n) <= A287648(n). - Eduard I. Vatutin, Mar 04 2023

Links

Table of n, a(n) for n=1..9.

Eduard I. Vatutin, About the spectra of numerical characteristics of orthogonal diagonal Latin squares of orders 1-11 (in Russian).

Eduard I. Vatutin, Proving list (best known examples).

E. I. Vatutin, N. N. Nikitina, M. O. Manzuk, A. M. Albertyan, and I. I. Kurochkin, On the construction of spectra of fast-computable numerical characteristics for diagonal Latin squares of small order, Intellectual and Information Systems (Intellect - 2021), Tula, 2021, pp. 7-17. (in Russian)

Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A287647, A287648, A305570, A305571, A349199, A354068.

Sequence in context: A178219 A322232 A232397 * A375943 A122753 A016714

Adjacent sequences: A360217 A360218 A360219 * A360221 A360222 A360223

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Jan 30 2023

Status

approved