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Location: AENC/resampling_chain/diagram_circle_lemma.tex - annotation
83372538681f
2.2 KiB
text/x-tex
simplified proof
aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 c2fa910c4916 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 c2fa910c4916 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 c2fa910c4916 aad4326b06f9 aad4326b06f9 aad4326b06f9 c2fa910c4916 c2fa910c4916 c2fa910c4916 aad4326b06f9 aad4326b06f9 | \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 +(2.6,1);
\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 {$I\cap [{\color{gray}n}{-l},r]_0$};
\draw[anchor=west] (-1,-0.5) node {$I\setminus[{\color{gray}n}{-l},r]_0$};
% 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 {${\color{gray}n}{-l}$};
\draw ({4*\step}:\r+1) +(0.2,0.2) node {$r$};
%
% 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 {$\frac{n}{2}$};
% n-1
\draw ({-1*\step}:\r-0.3) +(-0.4,0) node {${\color{gray}n}{-1}$};
% i_*
\draw[->] ({10*\step}:\r-1) -- ({10*\step}:\r-0.2);
\draw ({10*\step}:\r-1) +(0.3,0) node {$i_*$};
% j
\draw[->] ({0*\step}:\r-1.3) -- ({0*\step}:\r-0.8);
\draw ({0*\step}:\r-1) +(-0.4,0) node {$j$};
\end{tikzpicture}
\end{document}
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