\NeedsTeXFormat{LaTeX2e}
\ProvidesPackage{causets}[2022/02/07 v1.2 Package to draw causal set diagrams]
%% Copyright 2020-2022 by C. Minz
%
% This work may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either version 1.3
% of this license or (at your option) any later version.
% The latest version of this license is in
% http://www.latex-project.org/lppl.txt
%
% This work has the LPPL maintenance status "maintained".
% 
% The current version of this package is 1.2.
%
% The current maintainer of this work is C. Minz.
% https://github.com/c-minz
%
% This work consists of the files causets.sty, causets.tex,  
% causets.pdf, causet_tikz_example1.tex, causet_tikz_example1.pdf, 
% causet_tikz_example2.tex, causet_tikz_example2.pdf

\RequirePackage{tikz}
\usepgflibrary{arrows.meta}

%% PGF keys:
\def\tikzcausetsset#1{\pgfqkeys{/tikz/causets}{#1}}
\pgfkeys{/tikz/causets/.search also={/tikz}}
% size options:
\tikzcausetsset{%
	tile size/.store in=\causetTileSize,
	tile size/.value required,
	region line width/.store in=\causetRegionLine,
	region line width/.value required,
	grid line width/.store in=\causetGridLine,
	grid line width/.value required,
	event size/.store in=\causetEventSize,
	event size/.value required,
	link width/.store in=\causetLinkWidth,
	link width/.value required,
	broken link gap/.store in=\causetBrokenLinkGap,
	broken link gap/.value required,
	text scale/.store in=\causetTextScale,
	text scale/.value required,
	tiny/.value forbidden,
	small/.value forbidden,
	normal/.value forbidden,
	large/.value forbidden,
	huge/.value forbidden,
	tiny/.style={%
		tile size=0.30ex,
		region line width=0.02ex,
		grid line width=0.01ex,
		event size=0.16ex,
		link width=0.05ex,
		broken link gap=0.15ex,
		text scale=0.16},
	small/.style={%
		tile size=0.60ex,
		region line width=0.04ex,
		grid line width=0.02ex,
		event size=0.32ex,
		link width=0.10ex,
		broken link gap=0.30ex,
		text scale=0.32},
	normal/.style={%
		tile size=0.90ex,
		region line width=0.06ex,
		grid line width=0.03ex,
		event size=0.48ex,
		link width=0.15ex,
		broken link gap=0.45ex,
		text scale=0.48},
	large/.style={%
		tile size=1.35ex,
		region line width=0.09ex,
		grid line width=0.05ex,
		event size=0.75ex,
		link width=0.20ex,
		broken link gap=0.60ex,
		text scale=0.75},
	huge/.style={%
		tile size=1.80ex,
		region line width=0.12ex,
		grid line width=0.07ex,
		event size=1.00ex,
		link width=0.25ex,
		broken link gap=0.75ex,
		text scale=1.00}
}
% color options:
\tikzcausetsset{%
	region color/.initial=black!75,
	grid color/.initial=black!25,
	tile color/.initial=black!10!white,
	event color/.initial=black,
	label color/.initial=black,
	link color/.initial=black!65!white,
	spatial link color/.initial=black!50!white,
	ulabel color/.initial=black!65!white,
	vlabel color/.initial=black!65!white,
	black colors/.style={%
		region color=black,
		grid color=black,
		tile color=white,
		event color=black,
		label color=black,
		link color=black,
		spatial link color=black,
		ulabel color=black,
		vlabel color=black},
	gray colors/.style={%
		region color=black!75,
		grid color=black!25,
		tile color=black!10!white,
		event color=black,
		label color=black,
		link color=black!65!white,
		spatial link color=black!50!white,
		ulabel color=black!65!white,
		vlabel color=black!65!white},
	blue colors/.style={%
		region color=black!75,
		grid color=black!25,
		tile color=cyan!25!black!25!white,
		event color=blue!50!black,
		label color=blue!50!black,
		link color=cyan!75!black,
		spatial link color=blue!75!white,
		ulabel color=black!50,
		vlabel color=black!50},
	neon colors/.style={%
		region color=green,
		grid color=green,
		tile color=yellow,
		event color=blue,
		label color=blue,
		link color=cyan,
		spatial link color=red,
		ulabel color=magenta,
		vlabel color=magenta}
}
% styles:
\newif\ifcausetsDrawPermutation
\newif\ifcausetsDrawLinks
\newif\ifcausetsBreakLinks
\newif\ifcausetsDrawSpatialLinks
\newif\ifcausetsDrawLabels
\newif\ifcausetsDrawULabels
\newif\ifcausetsDrawVLabels
\tikzcausetsset{%
	show permutation/.is if=causetsDrawPermutation,
	show links/.is if=causetsDrawLinks,
	break links/.is if=causetsBreakLinks,
	show spatial links/.is if=causetsDrawSpatialLinks,
	show labels/.is if=causetsDrawLabels,
	show ulabels/.is if=causetsDrawULabels,
	show vlabels/.is if=causetsDrawVLabels,
	permutation/.code={\causetsDrawPermutationtrue},
	linked/.code={\causetsDrawLinkstrue},
	unlinked/.code={\causetsDrawLinksfalse},
	brokenly linked/.code={\causetsBreakLinkstrue},
	continuously linked/.code={\causetsBreakLinksfalse},
	spatially linked/.code={\causetsDrawSpatialLinkstrue},
	spatially unlinked/.code={\causetsDrawSpatialLinksfalse},
	labeled/.code={\causetsDrawLabelstrue},
	unlabeled/.code={\causetsDrawLabelsfalse},
	labeled u/.code={\causetsDrawULabelstrue},
	unlabeled u/.code={\causetsDrawULabelsfalse},
	labeled v/.code={\causetsDrawVLabelstrue},
	unlabeled v/.code={\causetsDrawVLabelsfalse},
	every region/.value forbidden,
	every region/.style={color=\pgfkeysvalueof{/tikz/causets/region color}, line width=\causetRegionLine},
	region/.style={show permutation, every region/.append style={#1}},
	every grid/.value forbidden,
	every grid/.style={color=\pgfkeysvalueof{/tikz/causets/grid color}, line width=\causetGridLine, step=\causetTileSize},
	grid/.style={show permutation, every grid/.append style={#1}},
	every tile/.value forbidden,
	every tile/.style={color=\pgfkeysvalueof{/tikz/causets/tile color}, line width=\causetGridLine, fill},
	tiles/.style={show permutation, every tile/.append style={#1}},
	every event/.value forbidden,
	every event/.style={color=\pgfkeysvalueof{/tikz/causets/event color}, circle, fill, inner sep=0pt, minimum size=\causetEventSize},
	events/.value required,
	events/.style={every event/.append style={#1}},
	Link Start/.tip={},
	Link Pause/.tip={Triangle Cap[] . Fast Triangle[] . Fast Triangle[]},
	Link Resume/.tip={Triangle Cap[reversed] . Fast Triangle[reversed] . Fast Triangle[reversed]},
	Link End/.tip={},
	every link/.value forbidden,
	every link/.style={color=\pgfkeysvalueof{/tikz/causets/link color}, line width=\causetLinkWidth, {Link Start[]}-{Link End[]}},
	links/.style={show links, every link/.append style={#1}},
	link starts/.value required,
	link starts/.style={Link Start/.tip={#1}},
	link pauses/.value required,
	link pauses/.style={Link Pause/.tip={#1}},
	link resumes/.value required,
	link resumes/.style={Link Resume/.tip={#1}},
	link ends/.value required,
	link ends/.style={Link End/.tip={#1}},
	cap links/.value forbidden,
	cap links/.style={link starts={Triangle Cap[reversed]}, link ends={Triangle Cap[]}},
	arrow links/.value forbidden,
	arrow links/.style={link ends={Stealth[round, open, length=4*\causetLinkWidth, line width=\causetLinkWidth/3]}},
	every spatial link/.value forbidden,
	every spatial link/.style={every link, color=\pgfkeysvalueof{/tikz/causets/spatial link color}, dashed},
	spatial links/.style={show spatial links, every spatial link/.append style={#1}},
	every label base/.value forbidden,
	every label base/.style={text opacity=1.0, scale=\causetTextScale, inner sep=0.5*\causetTextScale ex},
	all labels/.style={every label base/.append style={#1}},
	every label/.value forbidden,
	every label/.style={every label base, color=\pgfkeysvalueof{/tikz/causets/label color}, below left},
	labels/.style={show labels, every label/.append style={#1}},
	every ulabel/.value forbidden,
	every ulabel/.style={every label base, color=\pgfkeysvalueof{/tikz/causets/ulabel color}, right, rotate=-45, align=left},
	ulabels/.style={show ulabels, every ulabel/.append style={#1}},
	every vlabel/.value forbidden,
	every vlabel/.style={every label base, color=\pgfkeysvalueof{/tikz/causets/vlabel color}, left, rotate=45, align=right}, 
	vlabels/.style={show vlabels, every vlabel/.append style={#1}},
	every causet/.value forbidden,
	every causet/.style={baseline=-0.707*\causetTileSize}
}

%% delare and execute options:
\tikzcausetsset{normal}
\causetsDrawLinkstrue
\causetsBreakLinkstrue
\causetsDrawULabelstrue
\causetsDrawVLabelstrue
\DeclareOption{tiny}{\tikzcausetsset{tiny}}
\DeclareOption{small}{\tikzcausetsset{small}}
\DeclareOption{large}{\tikzcausetsset{large}}
\DeclareOption{huge}{\tikzcausetsset{huge}}
\DeclareOption{gray}{\tikzcausetsset{gray colors}}
\DeclareOption{black}{\tikzcausetsset{black colors}}
\DeclareOption{blue}{\tikzcausetsset{blue colors}}
\DeclareOption{neon}{\tikzcausetsset{neon colors}}
\DeclareOption{gray colors}{\tikzcausetsset{gray colors}}
\DeclareOption{black colors}{\tikzcausetsset{black colors}}
\DeclareOption{blue colors}{\tikzcausetsset{blue colors}}
\DeclareOption{neon colors}{\tikzcausetsset{neon colors}}
\DeclareOption{linked}{\causetsDrawLinkstrue}
\DeclareOption{unlinked}{\causetsDrawLinksfalse}
\DeclareOption{cap linked}{\tikzcausetsset{cap links}}
\DeclareOption{arrow linked}{\tikzcausetsset{arrow links}}
\DeclareOption{brokenly linked}{\causetsBreakLinkstrue}
\DeclareOption{continuously linked}{\causetsBreakLinksfalse}
\DeclareOption{spatially linked}{\causetsDrawSpatialLinkstrue}
\DeclareOption{spatially unlinked}{\causetsDrawSpatialLinksfalse}
\DeclareOption{permutation}{\causetsDrawPermutationtrue}
\DeclareOption{labeled}{\causetsDrawLabelstrue}
\DeclareOption{unlabeled}{\causetsDrawLabelsfalse}
\DeclareOption{labeled u}{\causetsDrawULabelstrue}
\DeclareOption{unlabeled u}{\causetsDrawULabelsfalse}
\DeclareOption{labeled v}{\causetsDrawVLabelstrue}
\DeclareOption{unlabeled v}{\causetsDrawVLabelsfalse}
\DeclareOption*{\PackageWarning{causets}{The package causets does not support the option: \CurrentOption}}
\ProcessOptions\relax

%% functions:
% variables:
\newcounter{causet@i}
\newcounter{causet@j}
\newif\ifcauset@ItemFoundInList

% count the number of events:
\newcommand*{\causets@readCausetSize}[1]{%
\setcounter{causet@i}{0}%
\foreach \causet@p in {#1}{%
	\stepcounter{causet@i}%
}%
\pgfmathsetmacro\causet@N{\value{causet@i}}%
}

% define and draw events as (E#):
\newcommand*{\causets@drawEvents}[1]{%
\setcounter{causet@i}{0}
\foreach \causet@p in {#1}{%
	\stepcounter{causet@i}
	\pgfmathsetmacro\causet@e@U{\causet@p - 1.0}
	\pgfmathsetmacro\causet@e@V{\value{causet@i} - 1.0}
	\ifcausetsDrawPermutation
		\path[causets/.cd, every tile] ( \causet@e@U * \causetTileSize, \causet@e@V * \causetTileSize ) 
			rectangle +( \causetTileSize, \causetTileSize );
	\fi
	\pgfmathsetmacro\causet@e@U{\causet@p - 0.5}
	\pgfmathsetmacro\causet@e@V{\value{causet@i} - 0.5}
	\node[causets/.cd, every event] (E\causet@p) 
		at ( \causet@e@U * \causetTileSize, \causet@e@V * \causetTileSize ) 
		{};
}
}

% draw the permutation and the null coordinate labels:
\newcommand*{\causets@drawPermutation}[1]{%
\ifcausetsDrawPermutation
	\draw[causets/.cd, every grid] ( 0, 0 ) 
		grid ( \causet@N * \causetTileSize, \causet@N * \causetTileSize );
	\draw[causets/.cd, every region] ( 0, 0 ) 
		rectangle ( \causet@N * \causetTileSize, \causet@N * \causetTileSize );
	\setcounter{causet@i}{0}
	\foreach \causet@p in {#1}{%
		\stepcounter{causet@i}
		\ifcausetsDrawULabels
			\node[causets/.cd, every ulabel] (EUL\causet@p) 
				at ( \value{causet@i} * \causetTileSize - 0.5 * \causetTileSize, 0 ) 
				{\thecauset@i};
		\fi
		\ifcausetsDrawVLabels
			\node[causets/.cd, every vlabel] (EVL\causet@p) 
				at ( 0, \value{causet@i} * \causetTileSize - 0.5 * \causetTileSize ) 
				{\causet@p};
		\fi
	}
\fi
}

% draw the spatial links from the permutation:
\newcommand*{\causets@drawSpatialLinks}[1]{%
\ifcausetsDrawSpatialLinks
	\setcounter{causet@i}{0}
	\foreach \causet@p in {#1}{%
		\stepcounter{causet@i}
		\edef\causet@qBound{0}
		\setcounter{causet@j}{0}
		\foreach \causet@q in {#1}{%
			\stepcounter{causet@j}
			\ifnum\value{causet@j}>\value{causet@i}
				\ifnum\causet@q>\causet@qBound
					\ifnum\causet@p>\causet@q
						\draw[causets/.cd, every spatial link] (E\causet@q) -- (E\causet@p);
						\xdef\causet@qBound{\causet@q}
					\fi
				\fi
			\fi
		}
	}
\fi
}

% draw event labels:
\newcommand*{\causets@drawEventLabels}[1]{%
\ifcausetsDrawLabels
	\foreach \causet@p in {#1}{%
		\node[causets/.cd, every label] (EL\causet@p) 
			at (E\causet@p) {\causet@p};
	}
\fi
}

% draw a causet from a permutation:
\newcommand*{\drawpcauset}[1]{%
\causets@readCausetSize{#1}
\begin{scope}[rotate=45]
	\begin{scope}[xshift=-\causet@N * \causetTileSize / 2, 
	              yshift=-\causet@N * \causetTileSize / 2]
		\causets@drawEvents{#1}
		\causets@drawPermutation{#1}
		\ifcausetsDrawLinks
			\setcounter{causet@i}{0}
			\foreach \causet@p in {#1}{%
				\stepcounter{causet@i}
				\pgfmathsetmacro\causet@qBound{int(\causet@N + 1)}
				\setcounter{causet@j}{0}
				\foreach \causet@q in {#1}{%
					\stepcounter{causet@j}
					\ifnum\value{causet@j}>\value{causet@i}
						\ifnum\causet@q<\causet@qBound
							\ifnum\causet@p<\causet@q
								\draw[causets/.cd, every link] (E\causet@p) -- (E\causet@q);
								\xdef\causet@qBound{\causet@q}
							\fi
						\fi
					\fi
				}
			}
		\fi
		\causets@drawSpatialLinks{#1}
		\causets@drawEventLabels{#1}
	\end{scope}
\end{scope}
}

% draw a causet from a permutation and a link-pair list:
\newcommand*{\drawcauset}[2]{%
\causets@readCausetSize{#1}
\begin{scope}[rotate=45]
	\begin{scope}[xshift=-\causet@N * \causetTileSize / 2, 
	              yshift=-\causet@N * \causetTileSize / 2]
		\causets@drawEvents{#1}
		\causets@drawPermutation{#1}
		\ifcausetsDrawLinks
			\ifcausetsBreakLinks
				\foreach \causet@From/\causet@To in {#2}{%
					\pgfmathsetmacro\causet@dU{int(\causet@To) - int(\causet@From)}
					\setcounter{causet@i}{0}
					\foreach \causet@p in {#1}{%
						\ifnum\causet@p=\causet@To
							\pgfmathparse{int(\value{causet@i})}
							\xdef\causet@dV{\pgfmathresult}
						\fi
						\ifnum\value{causet@i}>0
							\stepcounter{causet@i}
						\fi
						\ifnum\causet@p=\causet@From
							\stepcounter{causet@i}
						\fi
					}
					\def\causet@LastBreak{0}
					\setcounter{causet@i}{0}
					\foreach \causet@p in {#1}{%
						\ifnum\causet@p=\causet@To
							\setcounter{causet@i}{0}
						\fi
						\pgfmathparse{and(\value{causet@i} > 0, int((\causet@p - \causet@From) * \causet@dV) == int(\causet@dU * \value{causet@i}))}
						\ifnum\pgfmathresult=1
							\ifnum\causet@LastBreak=0
								\draw[causets/.cd, every link, {Link Start}-{Link Pause}, shorten >=\causetBrokenLinkGap]
									(E\causet@From) -- (E\causet@p);
							\else
								\draw[causets/.cd, every link, {Link Resume}-{Link Pause}, shorten <=\causetBrokenLinkGap, shorten >=\causetBrokenLinkGap]
									(E\causet@LastBreak) -- (E\causet@p);
							\fi
							\xdef\causet@LastBreak{\causet@p}
						\fi
						\ifnum\value{causet@i}>0
							\stepcounter{causet@i}
						\fi
						\ifnum\causet@p=\causet@From
							\setcounter{causet@i}{1}
						\fi
					}
					\ifnum\causet@LastBreak>0
						\draw[causets/.cd, every link, {Link Resume}-{Link End}, shorten <=\causetBrokenLinkGap]
							(E\causet@LastBreak) -- (E\causet@To);
					\else
						\draw[causets/.cd, every link]
							(E\causet@From) -- (E\causet@To);
					\fi
				}
			\else
				\foreach \causet@From/\causet@To in {#2}{%
					\draw[causets/.cd, every link] (E\causet@From) -- (E\causet@To);
				}
			\fi
		\fi
		\causets@drawEventLabels{#1}
	\end{scope}
\end{scope}
}

% draw a causet from a permutation removes links given in a link-pair list:
\newcommand*{\drawrcauset}[2]{%
\causets@readCausetSize{#1}
\begin{scope}[rotate=45]
	\begin{scope}[xshift=-\causet@N * \causetTileSize / 2, 
	              yshift=-\causet@N * \causetTileSize / 2]
		\causets@drawEvents{#1}
		\causets@drawPermutation{#1}
		\ifcausetsDrawLinks
			\setcounter{causet@i}{0}
			\foreach \causet@p in {#1}{%
				\stepcounter{causet@i}
				\pgfmathsetmacro\causet@qBound{int(\causet@N + 1)}
				\setcounter{causet@j}{0}
				\foreach \causet@q in {#1}{
					\stepcounter{causet@j}
					\ifnum\value{causet@j}>\value{causet@i}
						\ifnum\causet@q<\causet@qBound
							\ifnum\causet@p<\causet@q
								\global\causet@ItemFoundInListfalse
								\foreach \causet@From/\causet@To in {#2}{%
									\pgfmathparse{and(int(\causet@From) == int(\causet@p), int(\causet@To) == int(\causet@q))}
									\ifnum\pgfmathresult=1
										\global\causet@ItemFoundInListtrue
									\fi
								}
								\ifcauset@ItemFoundInList
									% skip link
								\else
									\draw[causets/.cd, every link] (E\causet@p) -- (E\causet@q);
								\fi
								\xdef\causet@qBound{\causet@q}
							\fi
						\fi
					\fi
				}
			}
		\fi
		\causets@drawSpatialLinks{#1}
		\ifcausetsDrawSpatialLinks
			\foreach \causet@From/\causet@To in {#2}{%
				\draw[causets/.cd, every spatial link] (E\causet@From) -- (E\causet@To);
			}
		\fi
		\causets@drawEventLabels{#1}
	\end{scope}
\end{scope}
}

% insert a TikZ picture with a causet from a permutation:
\newcommand*{\pcauset}[2][]{%
\begin{tikzpicture}[causets/.cd, every causet, #1]\drawpcauset{#2}\end{tikzpicture}}

% insert a TikZ picture with a causet from a permutation and a link-pair list:
\newcommand*{\causet}[3][]{%
\begin{tikzpicture}[causets/.cd, every causet, #1]\drawcauset{#2}{#3}\end{tikzpicture}}

% insert a TikZ picture with a causet from a permutation removes links given 
% in a link-pair list:
\newcommand*{\rcauset}[3][]{%
\begin{tikzpicture}[causets/.cd, every causet, #1]\drawrcauset{#2}{#3}\end{tikzpicture}}

%% short-hand functions:
\providecommand{\causetspath}{.}

\newcommand*{\causetfile}[2][]{%
\includegraphics[#1]{\causetspath/#2}}

\newcommand*{\pcausetP}[2][]{%
{\causetsDrawPermutationtrue\pcauset[#1]{#2}}}

\newcommand*{\pcausetL}[2][]{%
{\causetsDrawLabelstrue\pcauset[#1]{#2}}}

\newcommand*{\pcausetX}[2][]{%
{\causetsDrawPermutationtrue\pcausetL[#1]{#2}}}
	
\newcommand*{\causetP}[3][]{%
{\causetsDrawPermutationtrue\causet[#1]{#2}{#3}}}

\newcommand*{\causetL}[3][]{%
{\causetsDrawLabelstrue\causet[#1]{#2}{#3}}}

\newcommand*{\causetX}[3][]{%
{\causetsDrawPermutationtrue\causetL[#1]{#2}{#3}}}
	
\newcommand*{\rcausetP}[3][]{%
{\causetsDrawPermutationtrue\rcauset[#1]{#2}{#3}}}

\newcommand*{\rcausetL}[3][]{%
{\causetsDrawLabelstrue\rcauset[#1]{#2}{#3}}}

\newcommand*{\rcausetX}[3][]{%
{\causetsDrawPermutationtrue\rcausetL[#1]{#2}{#3}}}

%% some standard causets:
\newcommand*{\causetFence}[2][]{%
\ifcase#2%
\or%=1
\pcauset[#1]{1,2}%
\or%=2
\pcauset[#1]{3,1,4,2}%
\or%=3
\pcauset[#1]{5,3,6,1,4,2}%
\or%=4
\pcauset[#1]{7,5,8,3,6,1,4,2}%
\or%=5
\pcauset[#1]{9,7,10,5,8,3,6,1,4,2}%
\or%=6
\pcauset[#1]{11,9,12,7,10,5,8,3,6,1,4,2}%
\or%=7
\pcauset[#1]{13,11,14,9,12,7,10,5,8,3,6,1,4,2}%
\or%=8
\pcauset[#1]{15,13,16,11,14,9,12,7,10,5,8,3,6,1,4,2}%
\or%=9
\pcauset[#1]{17,15,18,13,16,11,14,9,12,7,10,5,8,3,6,1,4,2}%
\or%=10
\pcauset[#1]{19,17,20,15,18,13,16,11,14,9,12,7,10,5,8,3,6,1,4,2}%
\fi%
}

\newcommand*{\causetClosedFence}[2][]{%
\ifcase#2%
\or%=1
\pcauset[#1]{1,2}%
\or%=2
\pcauset[#1]{2,1,4,3}%
\or%=3
\rcauset[#1]{4,2,6,1,5,3}{2/5}%
\or%=4
\rcauset[#1]{6,4,8,2,7,1,5,3}{2/5,4/7}%
\or%=5
\rcauset[#1]{8,6,10,4,9,2,7,1,5,3}{2/5,4/7,6/9}%
\or%=6
\rcauset[#1]{10,8,12,6,11,4,9,2,7,1,5,3}{2/5,4/7,6/9,8/11}%
\or%=7
\rcauset[#1]{12,10,14,8,13,6,11,4,9,2,7,1,5,3}{2/5,4/7,6/9,8/11,10/13}%
\or%=8
\rcauset[#1]{14,12,16,10,15,8,13,6,11,4,9,2,7,1,5,3}{2/5,4/7,6/9,8/11,10/13,12/15}%
\or%=9
\rcauset[#1]{16,14,18,12,17,10,15,8,13,6,11,4,9,2,7,1,5,3}{2/5,4/7,6/9,8/11,10/13,12/15,14/17}%
\or%=10
\rcauset[#1]{18,16,20,14,19,12,17,10,15,8,13,6,11,4,9,2,7,1,5,3}{2/5,4/7,6/9,8/11,10/13,12/15,14/17,16/19}%
\fi%
}

\newcommand*{\causetCrown}[1][]{%
\causetClosedFence[#1]{3}%
}
