diff --git a/diagram_circle_lemma.tex b/diagram_circle_lemma.tex new file mode 100644 index 0000000000000000000000000000000000000000..5c33d4cd31917f816e0f537f85f31a08df641310 --- /dev/null +++ b/diagram_circle_lemma.tex @@ -0,0 +1,74 @@ +\documentclass{standalone} +\usepackage[T1]{fontenc} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{parskip} +\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}; + \def\step{15}; + + % Line and circles + \foreach \a in {0,...,23} { + \draw[-] ({\a*\step}:\r) -- ({(\a+1)*\step}:\r); + \draw ({\a*\step}:\r) circle (0.05); + } + + % Red dots + \foreach \a in {2,3,6,8,9,10,11,14,15,17,20} { + \draw[fill,red] ({\a*\step}:\r) circle (0.09); + } + % Blue squares + \foreach \a in {2,3,20} { + \draw[fill,blue] ({\a*\step}:{\r-0.3})+(-0.1,-0.1) rectangle +(0.1,0.1); + } + % Green triangles + \foreach \a in {6,8,9,10,11,14,15,17} { + \draw[fill,green] ({\a*\step}:{\r-0.3}) +(-0.15,-0.1) -- +(0.15,-0.1) -- +(0,0.15); + } + + % Legend + \draw (-1,0)+(-0.5,-1) rectangle +(2.2,1); + \draw[fill,red] (-1.1,0.5) circle (0.09); + \draw[fill,blue] (-1.1,0) +(-0.1,-0.1) rectangle +(0.1,0.1); + \draw[fill,green] (-1.1,-0.5) +(-0.15,-0.1) -- +(0.15,-0.1) -- +(0,0.15); + \draw[anchor=west] (-1,0.5) node {$I$}; + \draw[anchor=west] (-1,0) node {$I_{\mathrm{in}(n-l,k)}$}; + \draw[anchor=west] (-1,-0.5) node {$I_{\mathrm{out}(n-l,k)}$}; + + + % Bigger circle + \foreach \a in {-5,...,3} { + \draw[-,dashed] ({\a*\step}:\r+1) -- ({(\a+1)*\step}:\r+1); + %\draw ({\a*\step}:\r+1) circle (0.05); + } + \draw ({-5*\step}:\r+1) +(0.2,-0.2) node {$n-l$}; + \draw ({4*\step}:\r+1) +(0.2,0.2) node {$k$}; + + + % + % Arrows with labels + % + + % 0 + \draw ({0*\step}:\r-0.3) node {$0$}; + % 1 + \draw ({1*\step}:\r-0.3) node {$1$}; + % n/2 + \draw ({12*\step}:\r-0.3) node {$\frac{n}{2}$}; + % i_* + \draw[->] ({10*\step}:\r-1) -- ({10*\step}:\r-0.2); + \draw ({10*\step}:\r-1) +(0.3,0) node {$i_*$}; + % n-1 + \draw ({-1*\step}:\r-0.3) +(-0.4,0) node {$n-1$}; +\end{tikzpicture} +\end{document}