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EXAMPLE
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For order n=5 there are 7 different multisets L(P) with codes listed below in format "code - multiset":
1 - {1,1,1,1,1},
2 - {1,1,1,2},
3 - {1,1,3},
4 - {1,2,2},
5 - {1,4},
6 - {2,3},
7 - {5}.
The diagonal Latin square
0 1 2 3 4
2 3 4 0 1
4 0 1 2 3
1 2 3 4 0
3 4 0 1 2
of order n=5 has all a(5)=7 possible different types of generalized symmetries:
1. Px=[0,1,2,3,4], Py=[0,1,2,3,4], Pv=[0,1,2,3,4] (trivial generalized symmetry), L(Px)={1,1,1,1,1}, L(Py)={1,1,1,1,1}, L(Pv)={1,1,1,1,1}, generalized symmetry type (1,1,1).
2. Px=[0,1,2,3,4], Py=[1,2,3,4,0], Pv=[1,2,3,4,0], L(Px)={1,1,1,1,1}, L(Py)={5}, L(Pv)={5}, generalized symmetry type (1,7,7).
3. Px=[0,4,3,2,1], Py=[0,4,3,2,1], Pv=[0,4,3,2,1], L(Px)={1,2,2}, L(Py)={1,2,2}, L(Pv)={1,2,2}, generalized symmetry type (4,4,4).
4. Px=[0,2,4,1,3], Py=[0,2,4,1,3], Pv=[0,2,4,1,3], L(Px)={1,4}, L(Py)={1,4}, L(Pv)={1,4}, generalized symmetry type (5,5,5).
5. Px=[1,2,3,4,0], Py=[0,1,2,3,4], Pv=[2,3,4,0,1], L(Px)={5}, L(Py)={1,1,1,1,1}, L(Pv)={5}, generalized symmetry type (7,1,7).
6. Px=[1,2,3,4,0], Py=[3,4,0,1,2], Pv=[0,1,2,3,4], L(Px)={5}, L(Py)={5}, L(Pv)={1,1,1,1,1}, generalized symmetry type (7,7,1).
7. Px=[1,2,3,4,0], Py=[1,2,3,4,0], Pv=[3,4,0,1,2], L(Px)={5}, L(Py)={5}, L(Pv)={5}, generalized symmetry type (7,7,7).
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