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

0,3

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).

Links

Table of n, a(n) for n=0..10.

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.

Example

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)

Crossrefs

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

Sequence in context: A064489 A081089 A180928 * A342998 A342997 A118391

Adjacent sequences: A366329 A366330 A366331 * A366333 A366334 A366335

Keyword

nonn,more,hard

Author

Eduard I. Vatutin, Oct 07 2023

Status

approved