The permutation 164253 can be shown in a 6 X 6 grid:
X . . . . .
. . . . . X
. . . X . .
. X . . . .
. . . . X .
. . X . . .
This permutation gives the following 4 semicyclic squares.
1 2 3 4 5 6 1 4 2 5 3 6 1 4 3 6 2 5 1 4 5 2 3 6
2 3 4 5 6 1 2 5 3 6 4 1 3 6 2 5 4 1 2 5 6 3 4 1
4 5 6 1 2 3 3 6 4 1 5 2 5 2 4 1 3 6 6 3 4 1 2 5
6 1 2 3 4 5 4 1 5 2 6 3 4 1 6 3 5 2 4 1 2 5 6 3
3 4 5 6 1 2 5 2 6 3 1 4 6 3 5 2 1 4 5 2 3 6 1 4
5 6 1 2 3 4 6 3 1 4 2 5 2 5 1 4 6 3 3 6 1 4 5 2
In the third example, moving one cell down and two across increases the cell value by 1 (cyclically) and in the fourth example the displacement is 3 rows down and 2 across. Symbols can then be rearranged to give 4 distinct semicyclic squares with the first row in ascending order.
|