The Magic Encyclopedia ™ DataBase

Panmagic squares order 9
(by Aale de Winkel)

(note: table is broad, suggest print in landscape if paper copy is wanted)
The authors study of order 9 panmagic squares (see encyclopedia article) is based upon a simple parametric model, below those parameters are listed wherewith this author reached regular panmagic squares. The Latin Square Components are fully listed as well as their diagonal row transformed, the latter are LSC's themselves, however they don't seem to combine with the regular. Also one can use other transformations to obtain other LSC's (pe. the pan-flip variants) if those do combine with the other sets one might get new panmagic squares. When combined amongst the set one probably obtains transformed versions of already obtained square.

LSC(a,b): LCi,j = [a (j % 3) + b (j div 3) + i] % 3 ; i,j ε [0,..,8]; a = 0 .. 2 ; b = 1 .. 2
(0 1) (0 2) (1 1) (1 2) (2 1) (2 2)
0 1 2 0 1 2 0 1 2
0 1 2 0 1 2 0 1 2
0 1 2 0 1 2 0 1 2
1 2 0 1 2 0 1 2 0
1 2 0 1 2 0 1 2 0
1 2 0 1 2 0 1 2 0
2 0 1 2 0 1 2 0 1
2 0 1 2 0 1 2 0 1
2 0 1 2 0 1 2 0 1
0 1 2 0 1 2 0 1 2
0 1 2 0 1 2 0 1 2
0 1 2 0 1 2 0 1 2
2 0 1 2 0 1 2 0 1
2 0 1 2 0 1 2 0 1
2 0 1 2 0 1 2 0 1
1 2 0 1 2 0 1 2 0
1 2 0 1 2 0 1 2 0
1 2 0 1 2 0 1 2 0
0 1 2 0 1 2 0 1 2
1 2 0 1 2 0 1 2 0
2 0 1 2 0 1 2 0 1
1 2 0 1 2 0 1 2 0
2 0 1 2 0 1 2 0 1
0 1 2 0 1 2 0 1 2
2 0 1 2 0 1 2 0 1
0 1 2 0 1 2 0 1 2
1 2 0 1 2 0 1 2 0
0 1 2 0 1 2 0 1 2
1 2 0 1 2 0 1 2 0
2 0 1 2 0 1 2 0 1
2 0 1 2 0 1 2 0 1
0 1 2 0 1 2 0 1 2
1 2 0 1 2 0 1 2 0
1 2 0 1 2 0 1 2 0
2 0 1 2 0 1 2 0 1
0 1 2 0 1 2 0 1 2
0 1 2 0 1 2 0 1 2
2 0 1 2 0 1 2 0 1
1 2 0 1 2 0 1 2 0
1 2 0 1 2 0 1 2 0
0 1 2 0 1 2 0 1 2
2 0 1 2 0 1 2 0 1
2 0 1 2 0 1 2 0 1
1 2 0 1 2 0 1 2 0
0 1 2 0 1 2 0 1 2
0 1 2 0 1 2 0 1 2
2 0 1 2 0 1 2 0 1
1 2 0 1 2 0 1 2 0
2 0 1 2 0 1 2 0 1
1 2 0 1 2 0 1 2 0
0 1 2 0 1 2 0 1 2
1 2 0 1 2 0 1 2 0
0 1 2 0 1 2 0 1 2
2 0 1 2 0 1 2 0 1
S = 9 [3 LSC(a,b)t + LSC(c,d)] + [3 LSC(e,f)t + LSC(g,h)]
(0,1) (0,1) (0,1) (0,2) (0,1) (1,1) (0,1) (1,2) (0,1) (2,1) (0,1) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,2) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (2,1) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,1) (1,2) (2,1)
(0,2) (0,1) (0,2) (0,2) (0,2) (1,1) (0,2) (1,2) (0,2) (2,1) (0,2) (2,2)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,2) (1,1) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,1) (1,2) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,1) (1,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,2) (1,1) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,1) (1,2) (2,1)
(0,1) (0,2) (1,2) (2,1)
(1,1) (0,1) (1,1) (0,2) (1,1) (1,1) (1,1) (1,2) (1,1) (2,1) (1,1) (2,2)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,2) (2,2)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (2,1)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,2) (2,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,2) (2,2)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (2,1)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (1,1) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,2) (2,2)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (1,1) (1,2)
(0,2) (1,1) (1,2) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,1) (2,1)
(1,2) (0,1) (1,2) (0,2) (1,2) (1,1) (1,2) (1,2) (1,2) (2,1) (1,2) (2,2)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,2) (1,1) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(0,2) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,1) (1,2) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,1) (1,1) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,1) (1,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (2,1) (2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (2,2)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,1) (1,2) (2,1)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,2) (2,1)
(2,1) (0,1) (2,1) (0,2) (2,1) (1,1) (2,1) (1,2) (2,1) (2,1) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,2) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (2,1)
(0,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,2) (2,2)
(0,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (2,1)
(0,2) (1,1) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,1) (1,2) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (1,2)
(2,2) (0,1) (2,2) (0,2) (2,2) (1,1) (2,2) (1,2) (2,2) (2,1) (2,2) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,2) (1,1) (1,2) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,1) (1,1) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,1) (1,1) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,2) (1,1) (1,2) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (1,1) (1,2)
S = 9 [3 LSC(a,b)t + LSC(c,d)] + [3 LSC(e,f)t + LSC(g,h)>]t
(0,1) (0,1) (0,1) (0,2) (0,1) (1,1) (0,1) (1,2) (0,1) (2,1) (0,1) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,2) (1,1) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,2) (2,2)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,2) (1,1) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(0,2) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (1,2) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,2) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,2) (1,1) (1,2) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,2) (0,1) (0,2) (0,2) (0,2) (1,1) (0,2) (1,2) (0,2) (2,1) (0,2) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,2) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,1) (1,2) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (2,1)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,1) (1,2) (2,1) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,1) (1,1) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (2,1)
(0,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,1) (1,1) (1,2) (2,2)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,1) (2,1)
(1,1) (1,2) (2,1) (2,2)
(0,1) (1,2) (2,1) (2,2)
(1,1) (0,1) (1,1) (0,2) (1,1) (1,1) (1,1) (1,2) (1,1) (2,1) (1,1) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (2,1) (2,2)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,1) (1,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,2) (2,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,2) (2,2)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,1) (1,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (2,1) (2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,2) (2,2)
(0,1) (1,2) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,2) (2,1) (2,2)
(1,2) (0,1) (1,2) (0,2) (1,2) (1,1) (1,2) (1,2) (1,2) (2,1) (1,2) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,2) (1,1) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (2,1)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,2) (1,1) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (2,1)
(0,2) (1,1) (2,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,1) (0,2) (2,1) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,1) (2,1) (2,2)
(2,1) (0,1) (2,1) (0,2) (2,1) (1,1) (2,1) (1,2) (2,1) (2,1) (2,1) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (1,1) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,2) (2,2)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (1,1) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,1) (1,1) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,2) (1,2) (2,2)
(0,1) (0,2) (1,1) (2,2)
(0,1) (0,2) (1,1) (1,2)
(2,2) (0,1) (2,2) (0,2) (2,2) (1,1) (2,2) (1,2) (2,2) (2,1) (2,2) (2,2)
(0,2)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,1) (1,2) (2,1)
(0,1)
(1,1)
(1,2)
(2,1)
(2,2)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,1) (1,2) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1)
(0,2)
(1,2)
(2,1)
(2,2)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (1,1) (1,2)
(0,2) (1,1) (1,2) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,1) (2,1)
(0,1)
(0,2)
(1,1)
(2,1)
(2,2)
(0,1) (0,2) (1,1) (1,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,1) (1,2) (2,1)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1)
(0,2)
(1,1)
(1,2)
(2,2)
(0,1) (0,2) (1,2) (2,1)
(0,2) (1,1) (1,2) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,1) (1,2)
(0,1)
(0,2)
(1,1)
(1,2)
(2,1)
(0,2) (1,1) (1,2) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (1,1) (2,1)
(0,1) (0,2) (1,2) (2,1)
(0,1) (0,2) (1,1) (1,2)
diagonal row transformed LSC(a,b) (components of diagonal row transformed squares)
it seems not possible to combine with non transformed LSC's
(0 1)d->r (0 2)d->r (1 1)d->r (1 2)d->r (2 1)d->r (2 2)d->r
0 1 2 1 2 0 2 0 1
2 0 2 0 1 0 1 2 1
1 0 1 2 1 2 0 2 0
1 2 0 2 0 1 0 1 2
0 1 0 1 2 1 2 0 2
2 1 2 0 2 0 1 0 1
2 0 1 0 1 2 1 2 0
1 2 1 2 0 2 0 1 0
0 2 0 1 0 1 2 1 2
0 1 2 2 0 1 1 2 0
2 0 0 1 2 2 0 1 1
1 1 2 0 0 1 2 2 0
2 0 1 1 2 0 0 1 2
1 2 2 0 1 1 2 0 0
0 0 1 2 2 0 1 1 2
1 2 0 0 1 2 2 0 1
0 1 1 2 0 0 1 2 2
2 2 0 1 1 2 0 0 1
0 2 1 1 0 2 2 1 0
0 2 2 1 0 0 2 1 1
0 0 2 1 1 0 2 2 1
1 0 2 2 1 0 0 2 1
1 0 0 2 1 1 0 2 2
1 1 0 2 2 1 0 0 2
2 1 0 0 2 1 1 0 2
2 1 1 0 2 2 1 0 0
2 2 1 0 0 2 1 1 0
0 2 1 2 1 0 1 0 2
0 2 0 2 1 2 1 0 1
0 1 0 2 0 2 1 2 1
2 1 0 1 0 2 0 2 1
2 1 2 1 0 1 0 2 0
2 0 2 1 2 1 0 1 0
1 0 2 0 2 1 2 1 0
1 0 1 0 2 0 2 1 2
1 2 1 0 1 0 2 0 2
0 0 0 1 1 1 2 2 2
1 1 2 2 2 0 0 0 1
2 0 0 0 1 1 1 2 2
1 1 1 2 2 2 0 0 0
2 2 0 0 0 1 1 1 2
0 1 1 1 2 2 2 0 0
2 2 2 0 0 0 1 1 1
0 0 1 1 1 2 2 2 0
1 2 2 2 0 0 0 1 1
0 0 0 2 2 2 1 1 1
1 1 0 0 0 2 2 2 1
2 1 1 1 0 0 0 2 2
2 2 2 1 1 1 0 0 0
0 0 2 2 2 1 1 1 0
1 0 0 0 2 2 2 1 1
1 1 1 0 0 0 2 2 2
2 2 1 1 1 0 0 0 2
0 2 2 2 1 1 1 0 0