File:Bijection 1234 abcd.pdf

No higher resolution available.

Bijection_1234_abcd.pdf ‎(383 × 322 pixels, file size: 12 KB, MIME type: application/pdf)

Captions

English

Add a one-line explanation of what this file represents

Summary[edit]

DescriptionBijection 1234 abcd.pdf	English: One of the 24 possible bijective maps from the set X = {1,2,3,4} to the set Y = {a,b,c,d}. — See File:Bijection_1234_abdc.pdf, File:Bijection_1234_acbd.pdf, File:Bijection_1234_acdb.pdf, File:Bijection_1234_adbc.pdf, File:Bijection_1234_adcb.pdf, File:Bijection_1234_bacd.pdf, File:Bijection_1234_badc.pdf, File:Bijection_1234_bcad.pdf, File:Bijection_1234_bcda.pdf, File:Bijection_1234_bdac.pdf, File:Bijection_1234_bdca.pdf, File:Bijection_1234_cabd.pdf, File:Bijection_1234_cadb.pdf, File:Bijection_1234_cbad.pdf, File:Bijection_1234_cbda.pdf, File:Bijection_1234_cdab.pdf, File:Bijection_1234_cdba.pdf, File:Bijection_1234_dabc.pdf, File:Bijection_1234_dacb.pdf, File:Bijection_1234_dbac.pdf, File:Bijection_1234_dbca.pdf, File:Bijection_1234_dcab.pdf, and File:Bijection_1234_dcba.pdf for the remaining maps. (The LaTeX source code shown here gives a script that will generate all 24 versions.)
Date	6 February 2015
Source	Own work
Author	Jochen Burghardt
Other versions	Svg versions: File:Bijection_1234_abdc svg.svg, File:Bijection_1234_acbd svg.svg, File:Bijection_1234_acdb svg.svg, File:Bijection_1234_adbc svg.svg, File:Bijection_1234_adcb svg.svg, File:Bijection_1234_bacd svg.svg, File:Bijection_1234_badc svg.svg, File:Bijection_1234_bcad svg.svg, File:Bijection_1234_bcda svg.svg, File:Bijection_1234_bdac svg.svg, File:Bijection_1234_bdca svg.svg, File:Bijection_1234_cabd svg.svg, File:Bijection_1234_cadb svg.svg, File:Bijection_1234_cbad svg.svg, File:Bijection_1234_cbda svg.svg, File:Bijection_1234_cdab svg.svg, File:Bijection_1234_cdba svg.svg, File:Bijection_1234_dabc svg.svg, File:Bijection_1234_dacb svg.svg, File:Bijection_1234_dbac svg.svg, File:Bijection_1234_dbca svg.svg, File:Bijection_1234_dcab svg.svg, and File:Bijection_1234_dcba svg.svg

LaTeX source Code

\documentclass[12pt]{article}
\usepackage[pdftex]{color}
\usepackage[paperwidth=65mm,paperheight=55mm]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{65mm}
\setlength{\textheight}{55mm}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\setlength{\unitlength}{1mm}
\pagestyle{empty}

\definecolor{cRan}      {rgb}{0.50,0.00,0.00}   % domain set
\definecolor{cRanMem}   {rgb}{0.90,0.00,0.00}   % domain set member
\definecolor{cDom}      {rgb}{0.00,0.00,0.50}   % range set
\definecolor{cDomMem}   {rgb}{0.00,0.00,0.90}   % range set member
\definecolor{cMap}      {rgb}{0.00,0.00,0.00}   % map arrow

% define ignoring commands
\newcommand{\abcd}[1]{}
\newcommand{\abdc}[1]{}
\newcommand{\acbd}[1]{}
\newcommand{\acdb}[1]{}
\newcommand{\adbc}[1]{}
\newcommand{\adcb}[1]{}
\newcommand{\bacd}[1]{}
\newcommand{\badc}[1]{}
\newcommand{\bcad}[1]{}
\newcommand{\bcda}[1]{}
\newcommand{\bdac}[1]{}
\newcommand{\bdca}[1]{}
\newcommand{\cabd}[1]{}
\newcommand{\cadb}[1]{}
\newcommand{\cbad}[1]{}
\newcommand{\cbda}[1]{}
\newcommand{\cdab}[1]{}
\newcommand{\cdba}[1]{}
\newcommand{\dabc}[1]{}
\newcommand{\dacb}[1]{}
\newcommand{\dbac}[1]{}
\newcommand{\dbca}[1]{}
\newcommand{\dcab}[1]{}
\newcommand{\dcba}[1]{}

% redefine selected command as identity
\renewcommand{\@@@@}[1]{#1}

% use with these unix sh commands to generate all 24 pdf images:

% for p in abcd abdc acbd acdb adbc adcb bacd badc bcad bcda bdac bdca \
%          cabd cadb cbad cbda cdab cdba dabc dacb dbac dbca dcab dcba
% do    sed "s/@@@@/$p/" <Bijection_1234.tex >Bijection_1234_$p.tex
%       pdflatex Bijection_1234_$p.tex
% done

\begin{document}
\begin{picture}(60,50)

% dom
\thicklines%
\textcolor{cDom}{\put(20,50){\makebox(0,0)[lt]{$X$}}}%
\textcolor{cDom}{\put(10,25){\oval(20,50)}}%
\textcolor{cDomMem}{\put(9.6,10){\circle*{1}}}%
\textcolor{cDomMem}{\put(9.6,20){\circle*{1}}}%
\textcolor{cDomMem}{\put(9.6,30){\circle*{1}}}%
\textcolor{cDomMem}{\put(9.6,40){\circle*{1}}}%
\textcolor{cDomMem}{\put(8,10){\makebox(0,0)[r]{$4$}}}%
\textcolor{cDomMem}{\put(8,20){\makebox(0,0)[r]{$3$}}}%
\textcolor{cDomMem}{\put(8,30){\makebox(0,0)[r]{$2$}}}%
\textcolor{cDomMem}{\put(8,40){\makebox(0,0)[r]{$1$}}}%

% ran
\textcolor{cRan}{\put(41,50){\makebox(0,0)[rt]{$Y$}}}%
\textcolor{cRan}{\put(50,25){\oval(20,50)}}%
\textcolor{cRanMem}{\put(50.1,10){\circle*{1}}}%
\textcolor{cRanMem}{\put(50.1,20){\circle*{1}}}%
\textcolor{cRanMem}{\put(50.1,30){\circle*{1}}}%
\textcolor{cRanMem}{\put(50.1,40){\circle*{1}}}%
\textcolor{cRanMem}{\put(52,10){\makebox(0,0)[l]{$d$}}}%
\textcolor{cRanMem}{\put(52,20){\makebox(0,0)[l]{$c$}}}%
\textcolor{cRanMem}{\put(52,30){\makebox(0,0)[l]{$b$}}}%
\textcolor{cRanMem}{\put(52,40){\makebox(0,0)[l]{$a$}}}%
\thinlines%

% mappings (all but one are ignored):
\abcd{%
\textcolor{cMap}{\put(10,10){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,20){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,30){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,40){\vector(1,0){40}}}%
}%
\abdc{%
\textcolor{cMap}{\put(10,10){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,40){\vector(1,0){40}}}%
}%
\acbd{%
\textcolor{cMap}{\put(10,10){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(1,0){40}}}%
}%
\acdb{%
\textcolor{cMap}{\put(10,10){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(1,0){40}}}%
}%
\adbc{%
\textcolor{cMap}{\put(10,10){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(2,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(1,0){40}}}%
}%
\adcb{%
\textcolor{cMap}{\put(10,10){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,30){\vector(2,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(1,0){40}}}%
}%
\bacd{%
\textcolor{cMap}{\put(10,10){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,20){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-1){40}}}%
}%
\badc{%
\textcolor{cMap}{\put(10,10){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-1){40}}}%
}%
\bcad{%
\textcolor{cMap}{\put(10,10){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,20){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-1){40}}}%
}%
\bcda{%
\textcolor{cMap}{\put(10,10){\vector(4,3){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-1){40}}}%
}%
\bdac{%
\textcolor{cMap}{\put(10,10){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(2,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-1){40}}}%
}%
\bdca{%
\textcolor{cMap}{\put(10,10){\vector(4,3){40}}}%
\textcolor{cMap}{\put(10,20){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,30){\vector(2,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-1){40}}}%
}%
\cabd{%
\textcolor{cMap}{\put(10,10){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(2,-1){40}}}%
}%
\cadb{%
\textcolor{cMap}{\put(10,10){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(2,-1){40}}}%
}%
\cbad{%
\textcolor{cMap}{\put(10,10){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,20){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,40){\vector(2,-1){40}}}%
}%
\cbda{%
\textcolor{cMap}{\put(10,10){\vector(4,3){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,40){\vector(2,-1){40}}}%
}%
\cdab{%
\textcolor{cMap}{\put(10,10){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(2,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(2,-1){40}}}%
}%
\cdba{%
\textcolor{cMap}{\put(10,10){\vector(4,3){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(2,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(2,-1){40}}}%
}%
\dabc{%
\textcolor{cMap}{\put(10,10){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-3){40}}}%
}%
\dacb{%
\textcolor{cMap}{\put(10,10){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-3){40}}}%
}%
\dbac{%
\textcolor{cMap}{\put(10,10){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-3){40}}}%
}%
\dbca{%
\textcolor{cMap}{\put(10,10){\vector(4,3){40}}}%
\textcolor{cMap}{\put(10,20){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,30){\vector(1,0){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-3){40}}}%
}%
\dcab{%
\textcolor{cMap}{\put(10,10){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,20){\vector(2,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-3){40}}}%
}%
\dcba{%
\textcolor{cMap}{\put(10,10){\vector(4,3){40}}}%
\textcolor{cMap}{\put(10,20){\vector(4,1){40}}}%
\textcolor{cMap}{\put(10,30){\vector(4,-1){40}}}%
\textcolor{cMap}{\put(10,40){\vector(4,-3){40}}}%
}%

\end{picture}
\end{document}

Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

to share – to copy, distribute and transmit the work
to remix – to adapt the work

Under the following conditions:

attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	18:16, 6 February 2015		383 × 322 (12 KB)	Jochen Burghardt (talk \| contribs)	User created page with UploadWizard

You cannot overwrite this file.

File usage on Commons

There are no pages that use this file.

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Software used	TeX
Conversion program	pdfTeX-1.40.3
Encrypted	no
Page size	184.252 x 155.905 pts
Version of PDF format	1.4

Structured data

File:Bijection 1234 abcd.pdf

Captions

Captions

Summary[edit]

Licensing[edit]

File history

File usage on Commons

Metadata

Structured data

Items portrayed in this file

depicts

creator

some value

copyright status

copyrighted

copyright license

Creative Commons Attribution-ShareAlike 4.0 International

inception

6 February 2015

source of file

original creation by uploader

media type

application/pdf

checksum

9ac917b0745f605afde47c2a10c1e8de16d47b64

data size

12,793 byte

height

322 pixel

width

383 pixel

number of pages

1

Navigation menu

File:Bijection 1234 abcd.pdf

Captions

Captions

Summary[edit]

Licensing[edit]

File history

File usage on Commons

Metadata

Navigation menu

Search