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

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

Offset

1,4

Comments

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

a(10) <= 668, a(11) <= 2091, a(12) <= 6240.

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

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. A287644, A287645, A344105, A350585.

Sequence in context: A327875 A158967 A253287 * A331814 A082170 A136377

Adjacent sequences: A357511 A357512 A357513 * A357515 A357516 A357517

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Oct 01 2022

Status

approved