File:Artin generators of the braid group.svg
Original file (SVG file, nominally 477 × 253 pixels, file size: 37 KB)
Captions
Summary[edit]
DescriptionArtin generators of the braid group.svg |
English: The figure shows the Artin generators of the braid group and a braid word. The inputs of the braid strands are numbered.
Русский: Изображены образующие Артина группы кос и косовое слово, составленное из них. Начальные кончики нитей пронумерованы. |
Date | |
Source | Own work |
Author | MauveAccueil |
LaTeX source[edit]
\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{braids}
\begin{document}
\begin{tikzpicture}[rotate=90,scale=0.8, every node/.style={scale=0.8}]
\draw[black,dashed] (0,0) grid ++(7,1);
\pic[
rotate=90,
line width=1.5pt,
braid/control factor=0,
braid/nudge factor=0,
braid/gap=0.11,
braid/number of strands = 6,
braid/height = 1cm,
name prefix=braid,
] at (1,-0.25) {braid={
s_3
}};
\node at (1,1+0.5) {$1$};
\node at (3,1+0.5) {$i$};
\node at (4,1+0.63) {$i+1$};
\node at (6,1+0.5) {$n$};
\node at (-0.5,0.5) {{\LARGE $\sigma_i$}};
\begin{scope}[shift={(0,-3)}]
\draw[black,dashed] (0,0) grid ++(7,1);
\pic[
rotate=90,
line width=1.5pt,
braid/control factor=0,
braid/nudge factor=0,
braid/gap=0.11,
braid/number of strands = 6,
braid/height = 1cm,
name prefix=braid,
] at (1,-0.25) {braid={
s_3^{-1}
}};
\node at (1,1+0.5) {$1$};
\node at (3,1+0.5) {$i$};
\node at (4,1+0.63) {$i+1$};
\node at (6,1+0.5) {$n$};
\node at (-0.5,0.4) {{\LARGE $\sigma_i^{-1}$}};
\begin{scope}[shift={(0,-3-5)}]
\draw[black,dashed] (0,0) grid ++(7,6);
\pic[
rotate=90,
line width=1.5pt,
braid/control factor=0,
braid/nudge factor=0,
braid/gap=0.11,
braid/number of strands = 6,
braid/height = 1cm,
name prefix=braid,
] at (1,-0.25) {braid={
s_5s_1^{-1}s_3s_3s_2s_5^{-1}
}};
\node at (1,6+0.5) {$1$};
\node at (2,6+0.5) {$2$};
\node at (3,6+0.5) {$3$};
\node at (4,6+0.5) {$4$};
\node at (5,6+0.5) {$5$};
\node at (6,6+0.5) {$6$};
\node at (-0.5,0.4+5) {{\LARGE $\sigma_5^{-1}$}};
\node at (-0.5-0.1,0.5+4) {{\LARGE $\sigma_2$}};
\node at (-0.5-0.1,0.5+3) {{\LARGE $\sigma_3$}};
\node at (-0.5-0.1,0.5+2) {{\LARGE $\sigma_3$}};
\node at (-0.5,0.4+1) {{\LARGE $\sigma_1^{-1}$}};
\node at (-0.5-0.1,0.5) {{\LARGE $\sigma_5$}};
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document}
Licensing[edit]
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:06, 8 February 2023 | 477 × 253 (37 KB) | MauveAccueil (talk | contribs) | Numbers enlarged | |
19:12, 6 February 2023 | 405 × 253 (37 KB) | MauveAccueil (talk | contribs) | paths export fixed | ||
18:07, 6 February 2023 | 432 × 270 (20 KB) | MauveAccueil (talk | contribs) | Uploaded own work with UploadWizard |
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Width | 381.5pt |
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Height | 202.41pt |