$$N=4$$

Partition of $$N-1$$

Characteristic term

1 1 1

$$\langle VPVPVPV\rangle$$

2 1

$$-\Delta E_1\langle V{P}^{2}VPV\rangle$$

1 2

$$-\Delta E_1\langle VPV{P}^{2}V\rangle$$

3

$${\left(\Delta E_1\right)}^2\langle V{P}^{3}V\rangle$$

$$N=5$$

Partition of $$N-1$$

Characteristic term

1 1 1 1

$$\langle VPVPVPVPV\rangle$$

2 1 1

$$-\Delta E_1\langle V{P}^{2}VPVPV\rangle$$

1 2 1

$$-\Delta E_1\langle VPV{P}^{2}VPV\rangle$$

1 1 2

$$-\Delta E_1\langle VPVPV{P}^{2}V\rangle$$

2 2

$${\left(\Delta E_1\right)}^2\langle V{P}^{2}V{P}^{2}V\rangle$$

3 1

$${\left(\Delta E_1\right)}^2\langle V{P}^{3}V{P}^{1}V\rangle$$

1 3

$${\left(\Delta E_1\right)}^2\langle VPV{P}^{3}V\rangle$$

4

$$-{\left(\Delta E_1\right)}^3\langle V{P}^{4}V\rangle$$

$$N=6$$

Partition of $$N-1$$

Characteristic term

1 1 1 1 1

$$\langle VPVPVPVPVPV\rangle$$

2 1 1 1

$$-\Delta E_1\langle V{P}^{2}VPVPVPV\rangle$$

1 2 1 1

$$-\Delta E_1\langle VPV{P}^{2}VPVPV\rangle$$

1 1 2 1

$$-\Delta E_1\langle VPVPV{P}^{2}VPV\rangle$$

1 1 1 2

$$-\Delta E_1\langle VPVPVPV{P}^{2}V\rangle$$

2 2 1

$${\left(\Delta E_1\right)}^2\langle V{P}^{2}V{P}^{2}VPV\rangle$$

2 1 2

$${\left(\Delta E_1\right)}^2\langle V{P}^{2}VPV{P}^{2}V\rangle$$

1 2 2

$${\left(\Delta E_1\right)}^2\langle VPV{P}^{2}V{P}^{2}V\rangle$$

3 1 1

$${\left(\Delta E_1\right)}^2\langle V{P}^{3}VPVPV\rangle$$

1 3 1

$${\left(\Delta E_1\right)}^2\langle VPV{P}^{3}VPV\rangle$$

1 1 3

$${\left(\Delta E_1\right)}^2\langle VPVPV{P}^{3}V\rangle$$

3 2

$$-{\left(\Delta E_1\right)}^3\langle V{P}^{3}V{P}^{2}V\rangle$$

2 3

$$-{\left(\Delta E_1\right)}^3\langle V{P}^{2}V{P}^{3}V\rangle$$

4 1

$$-{\left(\Delta E_1\right)}^3\langle V{P}^{4}VPV\rangle$$

1 4

$$-{\left(\Delta E_1\right)}^3\langle VPV{P}^{4}V\rangle$$

5

$${\left(\Delta E_1\right)}^4\langle V{P}^{5}V\rangle$$