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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

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$\sum\limits_{1 \leq i < j \leq 3}H(X_i,X_j)$.

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  • $\begingroup$ Is there any way to generalize the above?? I mean I want this sum when I am working with n = 3 (H(X1,X2,X3)). If I am working with n = 4 (H(X1,X2,X3,X4)) then I want the sum H(X1,X2,X3)+H(X1,X2,X4)+H(X1,X3,X4)+H(X2,X3,X4). Is there any way to generalize this sum for all n? $\endgroup$ – Dimitri C Mar 23 '15 at 11:07
  • $\begingroup$ $1 \leq i < j < k \leq 4$.. in general $1 \leq i_1 < i_2 < \dots <i_t \leq n$.. $\endgroup$ – vudu vucu Mar 23 '15 at 11:11
  • $\begingroup$ Is the above a triple sum?? $\endgroup$ – Dimitri C Mar 23 '15 at 11:13
  • $\begingroup$ $\sum\limits_{1 \leq i < j < k\leq 4}H(X_i,X_j,X_k)$. $\endgroup$ – vudu vucu Mar 23 '15 at 11:16

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