Table 2 Precomputed expressions used in the proof of Lemma 4.7

1

1

n - j

0

0

n - j

2

0

j - i + 1

1

1

j - i + 1

0

0

j - i + 1

${\displaystyle {\sum }_{l=2}^{r-1}{\displaystyle {\sum }_{k=1}^n{d}_S(x_l,x_k)}}$

${\displaystyle {\sum }_{l=1}^n{d}_S(x_r,x_l)}$

(j - 1)(n - j) + (r - j - 1)j

j

(r - 2)(n - j)

n - j

(j - i + 1)(n - 2j + 2i + r - 4)

j - i + 1

(i - 2)(j - i + 1) + (r - i)(i - 1 + n - j)

i - 1 + n - j

(r - 2)(j - i + 1)

j - i + 1