A357514 Minimum number of transversals in an orthogonal diagonal Latin square of order n.

1, 0, 0, 8, 15, 0, 23, 16, 132

Offset: 1

Author

Eduard I. Vatutin, Oct 01 2022

Keywords

• nonn
• more
• hard

Comments

Orthogonal diagonal Latin squares is a diagonal Latin squares that have at least one orthogonal diagonal mate.

a(10) <= 652, a(11) <= 2091, a(12) <= 6240. - Eduard I. Vatutin, Oct 01 2022, updated Oct 21 2024

Every diagonal Latin square is a Latin square and every orthogonal diagonal Latin square is a diagonal Latin square, so 0 <= A287645(n) <= a(n) <= A287644(n) <= A090741(n). - Eduard I. Vatutin, Feb 17 2023

Links

• Eduard I. Vatutin, About the spectra of numerical characteristics of orthogonal diagonal Latin squares of orders 1-11 (in Russian).
• Eduard I. Vatutin, 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. A287644, A287645, A344105, A350585.