1 V = (x1, x2, x0)

2 X = {x0, x1, x2}

3 Note that the ordering of the variables in X is the canonical ordering

4 (ascendingly according to their labels) but the ordering in V is different.

6 The permutation between both variable orderings is sigma = (2, 0, 1), or more verbosely:

7 sigma[0] = 2

8 sigma[1] = 0

9 sigma[2] = 1

10 This means that variable V[sigma[n]] should correspond with the n'th variable in X (for n=0,...,2)...OK.

12 The states of the variables x0,x1,x2 are, according to the ordering in V:

13 SV: x0: x1: x2:

14 0 0 0 0

15 1 0 1 0

16 2 0 2 0

17 3 0 0 1

18 4 0 1 1

19 5 0 2 1

20 6 1 0 0

21 7 1 1 0

22 8 1 2 0

23 9 1 0 1

24 10 1 1 1

25 11 1 2 1

27 The states of the variables x0,x1,x2 are, according to the canonical ordering in X:

28 SX: x0: x1: x2:

29 0 0 0 0

30 1 1 0 0

31 2 0 1 0

32 3 1 1 0

33 4 0 2 0

34 5 1 2 0

35 6 0 0 1

36 7 1 0 1

37 8 0 1 1

38 9 1 1 1

39 10 0 2 1

40 11 1 2 1

42 The permutation sigma induces the following permutation of linear indices of joint states:

43 SV: SX:

44 0 0

45 1 2

46 2 4

47 3 6

48 4 8

49 5 10

50 6 1

51 7 3

52 8 5

53 9 7

54 10 9

55 11 11