# How can I re-write $H(X_1,X_2)+H(X_2,X_3)+H(X_1,X_3)$ using $\sum$ notation?

How can I re-write $H(X_1,X_2)+H(X_2,X_3)+H(X_1,X_3)$ using $\sum$ notation?

Also how can I re-write $H(X_1,X_2,X_3)+H(X_1,X_2,X_4)+H(X_1,X_3,X_4)+ H(X_2,X_3,X_4)$ using $\sum$ notation?

Is there any way to generalize a sum so I can find any sum even if I want pairs of two , or pairs of 3 or pairs of any number?

Is $\sum H(X_i,X_j, j>i)$ correct? If yes what limits the sum will have? Thanks

$\sum\limits_{1 \leq i < j \leq 3}H(X_i,X_j)$.
• $1 \leq i < j < k \leq 4$.. in general $1 \leq i_1 < i_2 < \dots <i_t \leq n$.. – vudu vucu Mar 23 '15 at 11:11
• $\sum\limits_{1 \leq i < j < k\leq 4}H(X_i,X_j,X_k)$. – vudu vucu Mar 23 '15 at 11:16