Reduce size of sum sub/superscript?

Question

I have a text with lots of sums where the sub/superscripts are pretty long, as in

$\displaystyle\sum_{ k=1+min\{a-1,b-1\}}^{ max\{a-1,b-1\} } i_k$

and when I compile the text gets very ugly, since the size of the superscripts drag the $i_k$ part far to the right, not counting the whole empty space it creates between the sum itself...

I am trying to find a way to countour the situation, but writing $\displaystyle \sum_{{\tiny k=1+min\{a-1,b-1\}}}^{{\tiny max\{a-1,b-1\}}}i_k$ doesn't seem to be doing anything... Is there a way to reduce the font size so that it fits exactly in the length of the sum symbol?

Edit: minimal working example with normal and tiny (the $i_k$ is tossed all the way to the right due to the length of the sub/superscripts)

\documentclass[12pt,a4paper]{report}

\usepackage{amsmath}

\begin{document}

$\displaystyle \sum_{k=1+min{a-1,b-1}}^{max{a-1,b-1}}i_k$ \\
$\displaystyle \sum_{{\tiny k=1+min{a-1,b-1}}}^{{\tiny max{a-1,b-1}}}i_k$ \\ 

\end{document} 

Answer 1

You can use the \smashoperator command from mathtools , and also insist for using \scriptscriptstyle instead of scriptstyle, but there might be a legibility problem:

\documentclass{article}
\usepackage{mathtools} 

\begin{document}

$\displaystyle\smashoperator{\sum_{k=1+\min(a-1,b-1)}^{\max(a-1,b-1)}}i_k$ \bigskip

$\displaystyle\smashoperator{\sum_{\scriptscriptstyle k=1+\min(a-1,b-1)}^{\scriptscriptstyle\max(a-1,b-1)}}i_k$

\end{document} 

Answer 2

To reduce the amount of visual overload inflicted on your readers, I would proceed along the following lines:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
Put $\mu(a,b)=1+\min\{a-1,b-1\}$ and $\nu(a,b)=\max\{a-1,b-1\}$. Then
\[
\sum_{ k=\mu(a,b)}^{ \nu(a,b) } i_k
\]
is defined as \dots
\end{document}

Answer 3

You could simplify this a lot like this:

\documentclass[12pt,a4paper]{report}
\usepackage{amsmath}
\begin{document}

\[
 \sum_k i_k
\]
with $1+\min(a-1,b-1)\le k\le \max(a-1,b-1)$

\end{document}