I do not know if I can write this kinds things in equations in latex.

enter image description here


The two answers are both excellent. I do not know how to choose. They are both standard answers for me.

  • 3
    Welcome to TeX.SX! Using tikz, for example, it is possible to do things like this. Can you post a minimal working example to show what you have tried? People are more likely to help if you can given them something to work from -- at a minimum supplying your equations without the circled dots would be a good start. – Andrew Sep 20 at 3:59
  • I just saw your update. You should use Ruixi's answer, who was first. – marmot Sep 20 at 23:48
  • PS: if both answers are just exactly equally good, check if one of the authors has substantially less reputation than the other. – giusti Sep 21 at 2:52
up vote 13 down vote accepted

The coefficients remind me of Bell polynomials. The following solution is far from perfect, but it’s a start.

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}

\newcommand\xone{%
  \tikz{\fill (0pt,0pt) circle (1pt);}%
}
\newcommand\xtwo{%
  \tikz{\fill (0pt,0pt) circle (1pt);
        \fill (6pt,0pt) circle (1pt);
        \draw[densely dotted] (3pt,0pt) ellipse (5pt and 3pt);}%
}
\newcommand\xthree{%
  \tikz{\fill (0pt,0pt) circle (1pt);
        \fill (6pt,0pt) circle (1pt);
        \fill (3pt,5pt) circle (1pt);
        \draw[densely dotted,rounded corners] (-4pt,-3pt) -- (10pt,-3pt) -- (3pt,10pt) -- cycle;}%
}
\newcommand\xfour{%
  \tikz{\fill (0pt,0pt) circle (1pt);
        \fill (6pt,0pt) circle (1pt);
        \fill (0pt,6pt) circle (1pt);
        \fill (6pt,6pt) circle (1pt);
        \draw[densely dotted,rounded corners] (-3pt,-3pt) -- (9pt,-3pt) -- (9pt,9pt) -- (-3pt,9pt) -- cycle;}%
}


\begin{document}

\begin{alignat*}{4}
\langle x  \rangle & = \vcenter{\hbox{\xone}}  \\
\langle x^2\rangle & = \vcenter{\hbox{\xtwo}}
                       && + \, \vcenter{\hbox{\xone\hspace{4pt}\xone}} \\
\langle x^3\rangle & = \vcenter{\hbox{\xthree}}
                       && + 3 \, \vcenter{\hbox{$\begin{tabular}{@{}c@{}}\xone\\[-4pt]\xtwo\end{tabular}$}}
                       && + \vcenter{\hbox{$\begin{tabular}{@{}c@{}}\xone\\[-6pt]\xone\hspace{4pt}\xone\end{tabular}$}} \\
\langle x^4\rangle & = \vcenter{\hbox{\xfour}}
                       && + 4 \, \vcenter{\hbox{\xthree}}\vcenter{\hbox{\xone}}
                       && + 3 \, \vcenter{\hbox{$\begin{tabular}{@{}c@{}}\xtwo\\[-5pt]\xtwo\end{tabular}$}}
                          + 6 \, \vcenter{\hbox{$\begin{tabular}{@{}c@{}}\xone\hspace{4pt}\xone\\[-3pt]\xtwo\end{tabular}$}}
                          + \, \vcenter{\hbox{$\begin{tabular}{@{}c@{}}\xone\hspace{4pt}\xone\\[-6pt]\xone\hspace{4pt}\xone\end{tabular}$}}
\end{alignat*}

\end{document}

draw

Very similar to Ruixi Zhang's nice answer except that I use fit to draw the dashed contours. This spares you from entering too many explicit coordinates.

\documentclass{article}
\usepackage{amsmath,mathtools,braket}
\usepackage{tikz}
\usetikzlibrary{fit,shapes.geometric,positioning}
\tikzset{bullet/.style={circle,fill,inner sep=0pt,outer sep=0pt,minimum
size=4pt,node contents={}},elli/.style={ellipse,draw,densely dashed,node
contents={},inner sep=1pt}}
\begin{document}
\begin{align*}
 \Braket{x}&~=~\vcenter{\hbox{\tikz{\node[bullet];}}}\\
 \Braket{x^2}&~=~\vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];
 \node[elli,fit=(b1)(b2)];}}}+\vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];}}}\\
 \Braket{x^3}&~=~\vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];
 \path (b1) -- (b2) node(b3)[bullet,midway,above=1mm+2pt];
 \node[fit=(b1)(b2)(b3),inner ysep=1pt](f){};
 \draw[densely dashed] (f.south west) --(f.south east) -- ([yshift=2pt]f.north) -- cycle;}}}
 +3\vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];
 \path (b1) -- (b2) node(b3)[bullet,midway,above=1mm+2pt];
 \node[elli,fit=(b1)(b2)];}}}+\vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];
 \path (b1) -- (b2) node(b3)[bullet,midway,above=1mm+2pt];}}}\\
 \Braket{x^4}&~=~\vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];
 \node(b3)[above=1mm of b1,bullet];
 \node(b4)[above=1mm of b2,bullet];
 \node[draw,densely dashed,rounded corners,fit=(b1)(b2)(b3)(b4)]{};}}}+4
 \vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];
 \path (b1) -- (b2) node(b3)[bullet,midway,above=1mm+2pt];
 \node(b4)[above right=1.5mm of b2,bullet];
 \node[fit=(b1)(b2)(b3),inner ysep=1pt](f){};
 \draw[densely dashed] (f.south west) --(f.south east) -- ([yshift=2pt]f.north) -- cycle;}}}
 +3\vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];
 \node(b3)[above=2mm of b1,bullet];
 \node(b4)[above=2mm of b2,bullet];
 \node[elli,fit=(b1)(b2)];
 \node[elli,fit=(b3)(b4)];
 }}}
 +6\vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];
 \node(b3)[above=2mm of b1,bullet];
 \node(b4)[above=2mm of b2,bullet];
 \node[elli,fit=(b1)(b2)];
 }}}
 +\vcenter{\hbox{\tikz{\node(b1)[bullet];
 \node(b2)[right=1mm of b1,bullet];
 \node(b3)[above=1mm of b1,bullet];
 \node(b4)[above=1mm of b2,bullet];}}} 
\end{align*}
\end{document}

enter image description here

Expanded on Ruixi Zhang's answer to make the actual equations easier to write and scale with document font size. Also added support for groups of dots bigger than 4.

sample

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}

% Begins dot group definition
% arg1 - num dots
\newcommand\bdots[1]{\!\:\tikz[baseline=-0.15ex]\bgroup
    \if#11
        \fill (0ex,0.5ex) circle (0.25ex);
    \fi
    \if#12
        \fill (0ex,0.5ex) circle (0.25ex);
        \fill (1ex,0.5ex) circle (0.25ex);
    \fi
    \if#13
        \fill (0ex,0ex) circle (0.25ex);
        \fill (1ex,0ex) circle (0.25ex);
        \fill (0.5ex,1ex) circle (0.25ex);
    \fi
    \ifnum#1>3
        \newcount\index
        \newdimen\offset
        \loop
            \advance\index by 2
            \fill (\offset,0ex) circle (0.25ex);
            \ifodd#1
                \ifnum\index<#1
                    \fill (\offset,1ex) circle (0.25ex);
                \fi
            \else
                \fill (\offset,1ex) circle (0.25ex);
            \fi
            \addtolength{\offset}{1ex}
            \ifnum\index<#1
        \repeat\fi
}
% Ends dot group definition
\newcommand\edots{\egroup}
% Circular border
% arg1 - num dots x-offset
% arg2 - num dots y-offset
\newcommand\bCirc[2]{
    \draw[densely dotted] (#1ex,#2ex) circle (0.5ex);
}
% Triangular border
\newcommand\bTrig{
    \draw[densely dotted,rounded corners=0.75ex] (-0.75ex,-0.5ex) -- (1.75ex,-0.5ex) -- (0.5ex,2ex) -- cycle;
}
% Rectangular blob border that accommodates odd number of dots
% arg1 - num dots x-offset
% arg2 - num dots y-offset
% arg3 - width in dots
% arg4 - height in dots
% arg5 - odd or even number of dots (0 or 1)
% arg6 - if arg5 is odd where to put the extra dot (note: arg1 does not include extra dots that are placed on the left)
%      ----- l to put it bottom left 
%      ----- L to put it top left
%      ----- r to put it bottom right
%      ----- R to put it top right
%      - if arg5 is even distributes two of the dots on either side
%      ----- n does not distribute
%      ----- Z to put top left and bottom right
%      ----- S to put bottom left and top right
%      ----- B to put bottom left and bottom right
%      ----- T to put top left and top right
\newcommand\bBlob[6]{
    \newdimen\Ax\setlength{\Ax}{-0.475ex}\addtolength{\Ax}{#1ex}
    \newdimen\Ay\setlength{\Ay}{-0.475ex}\addtolength{\Ay}{#2ex}
    \newdimen\Bx\setlength{\Bx}{0.475ex}\addtolength{\Bx}{#1ex}\addtolength{\Bx}{\dimexpr#3ex-1ex\relax}
    \newdimen\By\setlength{\By}{\Ay}
    \newdimen\Cx\setlength{\Cx}{\Bx}
    \newdimen\Cy\setlength{\Cy}{0.475ex}\addtolength{\Cy}{#2ex}\addtolength{\Cy}{\dimexpr#4ex-1ex\relax}
    \newdimen\Dx\setlength{\Dx}{\Ax}
    \newdimen\Dy\setlength{\Dy}{\Cy}
    \ifodd#5
        \newdimen\Ex
        \newdimen\Ey
        \newdimen\Fx
        \newdimen\Fy
        \if#6r
            \setlength{\Ex}{\Cx}\addtolength{\Ex}{-1ex}
            \setlength{\Ey}{\Cy}
            \setlength{\Fx}{\Dx}
            \setlength{\Fy}{\Dy}
            \addtolength{\Cy}{-1ex}
            \setlength{\Dx}{\Ex}
            \setlength{\Dy}{\Cy}
        \fi
        \if#6R
            \setlength{\Ex}{\Cx}
            \setlength{\Ey}{\Cy}
            \setlength{\Fx}{\Dx}
            \setlength{\Fy}{\Dy}
            \addtolength{\Bx}{-1ex}
            \setlength{\Cx}{\Bx}
            \setlength{\Cy}{\Ey}\addtolength{\Cy}{-1ex}
            \setlength{\Dx}{\Ex}
            \setlength{\Dy}{\Cy}
        \fi
        \if#6l
            \addtolength{\Dx}{1ex}
            \setlength{\Ex}{\Dx}
            \setlength{\Ey}{\Dy}\addtolength{\Ey}{-1ex}
            \setlength{\Fx}{\Ax}
            \setlength{\Fy}{\Ey}
        \fi
        \if#6L
            \setlength{\Ex}{\Dx}
            \setlength{\Ey}{\Dy}\addtolength{\Ey}{-1ex}
            \addtolength{\Ax}{1ex}
            \setlength{\Fx}{\Ax}
            \setlength{\Fy}{\Ey}
        \fi
        \draw[densely dotted,rounded corners=0.5ex] (\Ax,\Ay) -- (\Bx,\By) -- (\Cx,\Cy) -- (\Dx,\Dy) -- (\Ex,\Ey) -- (\Fx,\Fy) -- cycle;
    \else
        \if#6n
            \draw[densely dotted,rounded corners=0.5ex] (\Ax,\Ay) -- (\Bx,\By) -- (\Cx,\Cy) -- (\Dx,\Dy) -- cycle;
        \else
            \newdimen\Ex\setlength{\Ex}{\Cx}
            \newdimen\Ey\setlength{\Ey}{\Cy}
            \newdimen\Fx\setlength{\Fx}{\Dx}
            \newdimen\Fy\setlength{\Fy}{\Dy}
            \if#6Z
                \addtolength{\Ax}{1ex}
                \addtolength{\Cy}{-1ex}
                \addtolength{\Ex}{-1ex}
            \fi
            \if#6S
                \addtolength{\Bx}{-1ex}
                \addtolength{\Cx}{-1ex}
                \addtolength{\Cy}{-1ex}
                \addtolength{\Fx}{1ex}
            \fi
            \if#6B
                \addtolength{\Cy}{-1ex}
                \addtolength{\Ex}{-1ex}
                \addtolength{\Fx}{1ex}
            \fi
            \if#6T
                \addtolength{\Ax}{1ex}
                \addtolength{\Bx}{-1ex}
                \addtolength{\Cx}{-1ex}
                \addtolength{\Cy}{-1ex}
            \fi
            \setlength{\Dx}{\Ex}
            \setlength{\Dy}{\Cy}
            \newdimen\Gx\setlength{\Gx}{\Fx}
            \newdimen\Gy\setlength{\Gy}{\Dy}
            \newdimen\Hx\setlength{\Hx}{\Ax}
            \newdimen\Hy\setlength{\Hy}{\Dy}
            \draw[densely dotted,rounded corners=0.5ex] (\Ax,\Ay) -- (\Bx,\By) -- (\Cx,\Cy) -- (\Dx,\Dy) -- (\Ex,\Ey) -- (\Fx,\Fy) -- (\Gx,\Gy) -- (\Hx,\Hy) -- cycle;
        \fi
    \fi
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Shortcuts for various kinds of blob borders
% arg1 - num dots x-offset
% arg2 - num dots y-offset
% arg3 - width in dots
% arg4 - height in dots
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Rectangular border, for example:
% ## or ## or #
% ##          #
\newcommand\bRect[4]{
    \bBlob{#1}{#2}{#3}{#4}{0}{n}
}
% Lower-left blob, for example:
%  #
% ##
\newcommand\blBlob[4]{
    \bBlob{#1}{#2}{#3}{#4}{1}{l}
}
% Upper-left blob, for example:
% ##
%  #
\newcommand\bLBlob[4]{
    \bBlob{#1}{#2}{#3}{#4}{1}{L}
}
% Lower-right blob, for example:
% #
% ##
\newcommand\brBlob[4]{
    \bBlob{#1}{#2}{#3}{#4}{1}{r}
}
% Upper-right blob, for example:
% ##
% #
\newcommand\bRBlob[4]{
    \bBlob{#1}{#2}{#3}{#4}{1}{R}
}
% S blob, for example:
%  ##
% ##
\newcommand\bSBlob[4]{
    \bBlob{#1}{#2}{#3}{#4}{0}{S}
}
% Z blob, for example:
% ##
%  ##
\newcommand\bZBlob[4]{
    \bBlob{#1}{#2}{#3}{#4}{0}{Z}
}
% Top blob, for example:
% ###
%  #
\newcommand\bTBlob[4]{
    \bBlob{#1}{#2}{#3}{#4}{0}{T}
}
% Bottom blob, for example:
%  #
% ###
\newcommand\bBBlob[4]{
    \bBlob{#1}{#2}{#3}{#4}{0}{B}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Shortcut command for grouped dots
% arg1 - number of dots
\newcommand\gdots[1]{
    \bdots{#1}\edots
}
% Shortcut command for grouped dots w/border
% arg1 - number of dots
\newcommand\gdotsb[1]{
    \bdots{#1}
    \if#11
        \bCirc{0}{0.5}
    \fi
    \if#12
        \bRect{0}{0.5}{2}{1}
    \fi
    \if#13
        \bTrig
    \fi
    \ifnum#1>3
        \ifodd#1
            \brBlob{0}{0}{\numexpr(#1+1)/2\relax}{2}
        \else
            \bRect{0}{0}{\numexpr#1/2\relax}{2}
        \fi
    \fi
    \edots
}

\begin{document}

\begin{align*}
\langle x^1\rangle &= \gdots{1} \\
\langle x^2\rangle &= \gdotsb{2} + \gdots{2} \\
\langle x^3\rangle &= \gdotsb{3} + 3\bdots{3}\bRect{0}{0}{2}{1}\edots + \gdots{3} \\
\langle x^4\rangle &= 1\gdotsb{4} + 4\bdots{4}\brBlob{0}{0}{2}{2}\edots + 3\bdots{4}\bRect{0}{0}{2}{1}\bRect{0}{1}{2}{1}\edots + 6\bdots{4}\bRect{0}{0}{2}{1}\edots + \gdots{4} \\
\text{more} &: \gdotsb{1}, \bdots{4}\bRect{0}{0}{1}{2}\bRect{1}{0}{1}{2}\edots, \gdotsb{6}, \gdotsb{5}, \bdots{30}\brBlob{0}{0}{2}{2}\bLBlob{1}{0}{2}{2}\bRBlob{3}{0}{2}{2}\blBlob{4}{0}{2}{2}\bZBlob{6}{0}{3}{2}\bTBlob{8}{0}{3}{2}\bSBlob{10}{0}{3}{2}\bBBlob{12}{0}{3}{2}\bCirc{6}{0}\bCirc{14}{1}\edots
\end{align*}

\end{document}

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