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
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).
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
KEYWORD
nonn,more,hard
AUTHOR
Eduard I. Vatutin, Oct 07 2023
STATUS
approved