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Location: AENC/resampling_chain/diagram_groups.tex

András Gilyén
simplified proof
\documentclass{standalone}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{parskip}
\usepackage{marvosym} %Lightning symbol
\usepackage[usenames,dvipsnames]{color}
\usepackage[hidelinks]{hyperref}
\renewcommand*{\familydefault}{\sfdefault}

\usepackage{bbm} %For \mathbbm{1}
%\usepackage{bbold}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[scale=0.8]
    \def\r{4};

    % Line and circles
    \foreach \a in {0,...,23} {
        \draw[-] ({\a*15}:\r) -- ({(\a+1)*15}:\r);
        \draw ({\a*15}:\r) circle (0.05);
    }

    % Red dots
    \foreach \a in {-3,0,2,3,4,5,6} {
        \draw[fill,red] ({\a*15}:\r) circle (0.07);
    }
    % Red label
    \draw [fill,red] ({1*15}:\r/2) circle (0.07);
    \draw ({1*15}:\r/2) +(0,-0.3) node {zeroes of $b_2$};

    % Blue squares
    \foreach \a in {9,10,11,14,16,17} {
        \draw[fill,blue] ({\a*15}:\r) +(-0.15,-0.1) -- +(0.15,-0.1) -- +(0,0.15);
    }
    % Blue label
    \draw[fill,blue] ({11*15}:\r/2) +(-0.15,-0.1) -- +(0.15,-0.1) -- +(0,0.15);
    \draw ({11*15}:\r/2) +(0,-0.3) node {zeroes of $b_1$};

    % Arrows
    \draw[->] ({7*15}:\r-1) -- ({7*15}:\r-0.2);
    \draw[->] ({20*15}:\r-1) -- ({20*15}:\r-0.2);
    % Labels j1 j2
    \draw ({7*15}:\r-1) +(0,-0.2) node {$j_1$};
    \draw ({20*15}:\r-1) +(0,+0.2) node {$j_2$};

\end{tikzpicture}
\end{document}