dims

Steps Taken Along Each Dimension―k^th partition is the origin

2D Case (min path)

2D Case (max path)

3D Case (min path)

3D Case (max path)

x₁

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

x₂

0

0

0

1

1

1

1

1

1

1

1

0

0

0

0

0

0

1

1

1

1

1

1

1

1

0

0

0

x₃

0

0

0

0

0

1

1

1

1

0

0

0

0

0

Coordinates Of Path Along Each Dimension―k^th partition is the origin

2D Case (min path)

2D Case (max path)

3D Case (min path)

3D Case (max path)

x₁

1

2

3

4

5

6

7

1

2

3

4

5

6

7

1

2

3

4

5

6

7

1

2

3

4

5

6

7

x₂

0

0

0

1

2

3

4

1

2

3

4

4

4

4

0

0

0

1

2

3

4

1

2

3

4

4

4

4

x₃

Ý x₂ holds at 4

0

0

0

0

0

1

2

1

2

2

2

2

2

2

Ý x₃ holds at 2

Ý x₂ holds at 4

ΣL1

1

3

6

11

18

27

38

2

6

12

20

29

39

50

1

3

6

11

18

28

41

3

9

17

27

38

50

63