//European Example. The hierarchy of blocks.
//Please view in a non-proportional font such as Lucida Console.
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THE BLOCK SYSTEM FOR LEVEL 1.
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This block system is obtained from the 596 legal permutations for level 1 listed in file EELevel1Permutations.txt
It contains a total of 14 blocks. The reader can verify that this block system is invariant for all 596 permutations.
L1 BLOCKS: (2 8)(3 7)(0 6 10)(4 5)(1 9)(11 13 14)(12 15 16)(17)(18 19 22)(21 20 23)(24)(25 26 28)(30 27)(29 31 32)
L1 RENAME: A B C D E F G H I J K L M N
ORDER T T T N T N N - N N - N N T
The blocks in the system have been assigned names for the purpose of reference, as indicated.
These blocks become the elements of the causal set for level 2.
The row "ORDER" is explained below.
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THE INDUCTION AND ENCAPSULATION OF PRECEDENCE RELATIONS FROM LEVEL 1 INTO THE BLOCK SYSTEM OF LEVEL 1
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For the purpose of generating the causal set for level 2, it is necessary to calculate the precedence relations for
the blocks of level 1. They are obtained by induction (resulting in inter-block relations) or encapsulation (resulting
in intra-block relations) of the precedence relations from level 1. Only the induced relations are indicated below.
Reverse for level 1 elements/blocks.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
C E A B D D C B A E C F G F F G G H I I J J I J K L L M L N M N N
PRECEDENCE RELATIONS INTER-BLOCK INTRA-BLOCK RELATIONS
IN LEVEL 1 RELATIONS (ENCAPSULATED)
0 < 4 5 6 10 C < D 0 < 6 0 < 10
1 < 9 14 E < F 1 < 9
2 < 8 10 A < C 2 < 8
3 < 7 10 B < C 3 < 7
4 < 9 13 D < E F -
5 < 9 11 D < E F -
6 < 10 - 6 < 10
7 < 10 B < C -
8 < 10 A < C -
9 < 11 13 14 E < F -
10 < 11 13 14 C < F -
11 < 12 F < G -
12 < 17 18 G < H I -
13 < 15 F < G -
14 < 16 F < G -
15 < 17 19 G < H I -
16 < 17 22 G < H I -
17 < 18 19 22 H < I -
18 < 20 I < J -
19 < 21 I < J -
20 < 24 25 J < K L -
21 < 24 28 J < K L -
22 < 23 I < J -
23 < 24 26 J < K L -
24 < 25 26 28 K < L -
25 < 27 L < M -
26 < 29 L < N -
27 < 31 M < N -
28 < 30 L < M -
29 < 31 32 - 29 < 31 29 < 32
30 < 31 M < N -
31 < 32 - 31 < 32
Some inter-block relations are induced multiple times.
There are 18 independent inter-block precedence relations. They are:
{A