A366332 Minimum number of diagonal transversals in a semicyclic diagonal Latin square of order 2n+1.

1, 0, 5, 27, 0, 4523, 127339, 0, 204330233, 11232045257, 0

Offset: 0

Author

Eduard I. Vatutin, Oct 07 2023

Keywords

• nonn
• more
• hard

Comments

A horizontally semicyclic diagonal Latin square is a square where each row r(i) is a cyclic shift of the first row r(0) by some value d(i) (see example). Similarly, a vertically semicyclic diagonal Latin square is a square where each column c(i) is a cyclic shift of the first column c(0) by some value d(i).

Examples

			Example of horizontally semicyclic diagonal Latin square of order 13:
   0  1  2  3  4  5  6  7  8  9 10 11 12
   2  3  4  5  6  7  8  9 10 11 12  0  1  (d=2)
   4  5  6  7  8  9 10 11 12  0  1  2  3  (d=4)
   9 10 11 12  0  1  2  3  4  5  6  7  8  (d=9)
   7  8  9 10 11 12  0  1  2  3  4  5  6  (d=7)
  12  0  1  2  3  4  5  6  7  8  9 10 11  (d=12)
   3  4  5  6  7  8  9 10 11 12  0  1  2  (d=3)
  11 12  0  1  2  3  4  5  6  7  8  9 10  (d=11)
   6  7  8  9 10 11 12  0  1  2  3  4  5  (d=6)
   1  2  3  4  5  6  7  8  9 10 11 12  0  (d=1)
   5  6  7  8  9 10 11 12  0  1  2  3  4  (d=5)
  10 11 12  0  1  2  3  4  5  6  7  8  9  (d=10)
   8  9 10 11 12  0  1  2  3  4  5  6  7  (d=8)
		

Links

• Eduard I. Vatutin, About the spectra of numerical characteristics of different types of cyclic diagonal Latin squsres (in Russian).
• Eduard I. Vatutin, About the spectra of numerical characteristics of semicyclic diagonal Latin squares of order 17 (in Russian).
• Eduard I. Vatutin, About the spectra of numerical characteristics of semicyclic diagonal Latin squares of order 19 (in Russian).
• Eduard I. Vatutin, Proving list (best known examples).
• Index entries for sequences related to Latin squares and rectangles.

Crossrefs

Cf. A071607, A342990, A342997, A342998, A348212, A366331.