Summation subscript under summation symbol (\limits not working)

Question

I am trying to get the subscript in both summations in the following equation centered under the summation symbol:

\displaystyle \Phi(H) = \min { \sum_{\substack{i \in S \\ j \notin S}} w_{ij}  \over {\sum_{\substack{i \in S}} \pi_i} }

I have reached the above syntax result, which compiles without error but doesn't output what I am looking for, by following the links below:

Sums in math mode: how to display index under the sigma sign?

Separate long math text under sum symbol into different lines?

\limits doesn't seem to work, i.e the expression:

\[ \displaystyle \Phi(H) = \min { \sum_{\limits{\substack{i \in S \\ j \notin S}}} w_{ij}  \over {\sum_{\limits{i \in S}} \pi_i} } \]

gives the following error message: Limit controls must follow a math operator

If possible, I would like this to work for both inline and displayed formulas

don't use $$ or \over in latex, both are tex primitives which are somewhat hard to disable but should never be used in latex documents. — David Carlisle, Feb 27 '22 at 10:48
but as the message says \limits has to follow an operator so \sum\limits_{...} — David Carlisle, Feb 27 '22 at 10:49
@DavidCarlisle Usage of \frac instead of \over noted. How should I change the above for the equation to render correctly? I only wrote the $$...$$ after reading this: https://math.meta.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference — aristeidis, Feb 27 '22 at 11:41
to show the equation use an image as in the accepted answer, we do not have mathjax running on this site, it would be confusing as it doesn't use tex — David Carlisle, Feb 27 '22 at 12:58

gernot · Accepted Answer · 2022-02-27T11:43:53.483

3

Put the \displaystyle in front of the \sums.

\documentclass{article}
\usepackage{amsmath}
\begin{document}
[
  \Phi(H) = \min \frac{\displaystyle\sum_{\substack{i \in S \ j \notin S}} w_{ij}}
                      {\displaystyle\sum_{\substack{i \in S}} \pi_i}
]
\end{document}

I recommend to put the sums into one line:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
[
  \Phi(H) = \min \bigg(\sum_{\substack{i \in S \ j \notin S}} w_{ij} \Big/
                       \sum_{\substack{i \in S}} \pi_i\bigg)

]
\end{document}

edited Feb 27 '22 at 11:43

answered Feb 27 '22 at 10:37

gernot

49,614

Possibly \Big/ would be better in the second case. – egreg Feb 27 '22 at 11:01
Thank you very much! Could you please elaborate on why \limits is not needed in this case? But looks like it is when writing it inline.. – aristeidis Feb 27 '22 at 11:33
@egreg Not just possibly ... thanks, modified. – gernot Feb 27 '22 at 11:45
@aristeidis When you use \[...\], then you are in \displaystyle, and the large prefix operators like sum and product put the limits above and below by default. See also https://tex.stackexchange.com/a/119328/110998 – gernot Feb 27 '22 at 11:51

score 1 · Answer 2 · answered Feb 27 '22 at 13:56

hm, limits works if they are in correct place (immediately after \sum):

\documentclass{article}
\usepackage{amsmath}
\begin{document}
[
  \Phi(H) = \min \frac{\sum\limits_{\substack{i \in S \ j \notin S}} w_{ij}}
                      {\sum\limits_{\substack{i \in S}} \pi_i}
]
\end{document}

score 1 · Answer 3 · answered Feb 27 '22 at 21:35

I will use a compact mode to denote the sum into the \min command.

\documentclass{article}
\usepackage{mathtools}
\usepackage[utf8]{inputenc}
\usepackage{eulervm}
\begin{document}
Let be $W=\displaystyle\sum_{\substack{i \in S \\ j \notin S}}{w_{ij}}$ and $T=\displaystyle\sum_{ i \in S}{\pi_{i}}$ we have:
\[
  \Phi(H) = \min \frac{W}{T}
\]
\end{document}

Summation subscript under summation symbol (\limits not working)

3 Answers3