# Better double parenthesis notation for multiset

In my combinatorics homework I use double parenthesis to represent a multiset. I have referred to all the answers under Multiset notation in LaTeX on how to build such a notation.

However, the double parenthesis looks good alone but when put together with a binomial, it looks very inconsistent.

I used the code that come from this answer https://tex.stackexchange.com/a/5825/91144, which utilizes a \genfrac with left(/right).

\def\multiset#1#2{\ensuremath{\left(\kern-.3em\left(\genfrac{}{}{0pt}{}{#1}{#2}\right)\kern-.3em\right)}}


Here are four problematic examples

\documentclass{article}

\def\multiset#1#2{\ensuremath{\left(\kern-.3em\left(\genfrac{}{}{0pt}{}{#1}{#2}\right)\kern-.3em\right)}}

\begin{document}

\verb~$\multiset{5}{k}+\multiset{5}{k-1}+\multiset{5}{k-4}$~ \\
$\multiset{5}{k}+\multiset{5}{k-1}+\multiset{5}{k-4}$

\verb~$\sum_{\substack{i+j=15\\i,j\geq0}}\binom{5}{i}\multiset{3}{j}$~ \\
$\sum_{\substack{i+j=15\\i,j\geq0}}\binom{5}{i}\multiset{3}{j}$

\verb~$ab\binom{5}{i}123\multiset{3}{j}cd$~ \\
$ab\binom{5}{i}123\multiset{3}{j}cd$

\verb~$\sum{\multiset{5}{k}\multiset{5}{k}}$~ \\
$\sum_{i=0}^{k}{\multiset{m}{i}\multiset{n}{k-i}}$

\end{document} 1. inconsistent height (inline mode)
2. inconsistent height with \binom (inline mode)
3. incorrect spacing, comparing to \binom (display mode)
4. inconsistent sizes (display mode)

What I wanted is a notation that looks just similar to \binom{n}{k}, i.e. size, shape, spacing, etc, while having two pair of parenthesis around. And I expect it to work both inline and in display mode. Thank you :)

• Source code for the examples? – egreg Nov 1 '15 at 21:36
• But this image of source code! Please make it so, that it can be copied in editor and test it. – Zarko Nov 1 '15 at 22:25
• @Zarko: here is it: lpaste.net/6732560716236062720 – Shou Ya Nov 1 '15 at 22:32
• @ShouYa, ok, why you not copy in your question as minimal working example (without line numbers ...) by this you will make to people here eaiery to help you. – Zarko Nov 1 '15 at 22:35
• The rules for the delimiter size in generalized fractions are different from those for \left and \right; this is particularly evident in text style. The difference in case 4 is because the - has a depth (you'd see the same with +). – egreg Nov 1 '15 at 23:11

## 2 Answers

Try this:

\documentclass[preview,border=5mm]{standalone}
\usepackage{mathtools}
\newcommand{\textmultiset}{\bigl(\!{\binom{#1}{#2}}\!\bigr)}
\newcommand{\displaymultiset}{\left(\!{\binom{#1}{#2}}\!\right)}
\newcommand\multiset{\mathchoice{\displaymultiset{#1}{#2}}
{\textmultiset{#1}{#2}}
{\textmultiset{#1}{#2}}
{\textmultiset{#1}{#2}}}
\begin{document}
some text $\multiset{5}{k}+\binom{5}{k-1}+\multiset{5}{k{+}1}$

\bigskip
some text $\sum_{\substack{i+j=15\\i,j\geq0}}\binom{5}{i}\multiset{3}{j}\multiset{3}{j+1}$

$ab\multiset{5}{i+1}123\binom{3}{j+1}cd$

$\sum_{i=0}^{k}{\multiset{m}{i}\binom{n}{k-i}}$
\end{document} • thank you for your answer. I'm still wondering if the spacing around the \multiset can be better. e.g. ab␣((5,i+1))␣123 looks wider than 123␣(3,j+1)␣cd. Should I just add some \! around the command or is there a better way to do this? – Shou Ya Nov 1 '15 at 23:57
• Instead of \! you can use TeX primitive \kern -<value>, where you set <value> according to your taste. For example, for display version of \multset you can try with \newcommand{\displaymultiset}{\left(\kern-5pt{\binom{#1}{#2}}\!\!\right)} and see, which distance (left or right) looks nicer to you. – Zarko Nov 2 '15 at 0:39

I get somewhat better results by tweaking @Zarko's answer to

\newcommand\multiset%
{\mathchoice{\left(\kern-0.5em{\binom{#1}{#2}}\kern-0.5em\right)}
{\bigl(\kern-0.3em{\binom{#1}{#2}}\kern-0.3em\bigr)}
{\bigl(\kern-0.3em{\binom{#1}{#2}}\kern-0.3em\bigr)}
{\bigl(\kern-0.3em{\binom{#1}{#2}}\kern-0.3em\bigr)}}


But e.g. 2^{\multiset{2}{3}} looks ugly (the inner () are a bit too low).