path_walks.tex
Paper I: Typed Operator Systems, Seed Rank, and Exact Packet Coordinates
path_walks.tex
This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.
1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,
2 every node/.style={font=\sffamily\small},line cap=round,line join=round]
3 \node[circle,draw,minimum size=7mm,fill=black!75,text=white] at (0.0000,1.8000) {$1$};
4 \draw[thick] (0.3700,1.8000) -- (0.8800,1.8000);
5 \node[circle,draw,minimum size=7mm,fill=white] at (1.2500,1.8000) {$2$};
6 \draw[thick] (1.6200,1.8000) -- (2.1300,1.8000);
7 \node[circle,draw,minimum size=7mm,fill=white] at (2.5000,1.8000) {$3$};
8 \draw[thick] (2.8700,1.8000) -- (3.3800,1.8000);
9 \node[circle,draw,minimum size=7mm,fill=white] at (3.7500,1.8000) {$4$};
10 \draw[thick] (4.1200,1.8000) -- (4.6300,1.8000);
11 \node[circle,draw,minimum size=7mm,fill=white] at (5.0000,1.8000) {$5$};
12 \filldraw[fill=black!78,draw=white,line width=.8pt] (0.8750,0.7000) rectangle ++(0.6500,-0.6500);
13 \node[text=white,font=\scriptsize] at (1.2000,0.3750) {$1$};
14 \filldraw[fill=black!5,draw=white,line width=.8pt] (1.5250,0.7000) rectangle ++(0.6500,-0.6500);
15 \node[text=black!45,font=\scriptsize] at (1.8500,0.3750) {$0$};
16 \filldraw[fill=black!78,draw=white,line width=.8pt] (2.1750,0.7000) rectangle ++(0.6500,-0.6500);
17 \node[text=white,font=\scriptsize] at (2.5000,0.3750) {$1$};
18 \filldraw[fill=black!5,draw=white,line width=.8pt] (2.8250,0.7000) rectangle ++(0.6500,-0.6500);
19 \node[text=black!45,font=\scriptsize] at (3.1500,0.3750) {$0$};
20 \filldraw[fill=black!78,draw=white,line width=.8pt] (3.4750,0.7000) rectangle ++(0.6500,-0.6500);
21 \node[text=white,font=\scriptsize] at (3.8000,0.3750) {$2$};
22 \filldraw[fill=black!5,draw=white,line width=.8pt] (0.8750,0.0500) rectangle ++(0.6500,-0.6500);
23 \node[text=black!45,font=\scriptsize] at (1.2000,-0.2750) {$0$};
24 \filldraw[fill=black!78,draw=white,line width=.8pt] (1.5250,0.0500) rectangle ++(0.6500,-0.6500);
25 \node[text=white,font=\scriptsize] at (1.8500,-0.2750) {$1$};
26 \filldraw[fill=black!5,draw=white,line width=.8pt] (2.1750,0.0500) rectangle ++(0.6500,-0.6500);
27 \node[text=black!45,font=\scriptsize] at (2.5000,-0.2750) {$0$};
28 \filldraw[fill=black!78,draw=white,line width=.8pt] (2.8250,0.0500) rectangle ++(0.6500,-0.6500);
29 \node[text=white,font=\scriptsize] at (3.1500,-0.2750) {$2$};
30 \filldraw[fill=black!5,draw=white,line width=.8pt] (3.4750,0.0500) rectangle ++(0.6500,-0.6500);
31 \node[text=black!45,font=\scriptsize] at (3.8000,-0.2750) {$0$};
32 \filldraw[fill=black!5,draw=white,line width=.8pt] (0.8750,-0.6000) rectangle ++(0.6500,-0.6500);
33 \node[text=black!45,font=\scriptsize] at (1.2000,-0.9250) {$0$};
34 \filldraw[fill=black!5,draw=white,line width=.8pt] (1.5250,-0.6000) rectangle ++(0.6500,-0.6500);
35 \node[text=black!45,font=\scriptsize] at (1.8500,-0.9250) {$0$};
36 \filldraw[fill=black!78,draw=white,line width=.8pt] (2.1750,-0.6000) rectangle ++(0.6500,-0.6500);
37 \node[text=white,font=\scriptsize] at (2.5000,-0.9250) {$1$};
38 \filldraw[fill=black!5,draw=white,line width=.8pt] (2.8250,-0.6000) rectangle ++(0.6500,-0.6500);
39 \node[text=black!45,font=\scriptsize] at (3.1500,-0.9250) {$0$};
40 \filldraw[fill=black!78,draw=white,line width=.8pt] (3.4750,-0.6000) rectangle ++(0.6500,-0.6500);
41 \node[text=white,font=\scriptsize] at (3.8000,-0.9250) {$3$};
42 \filldraw[fill=black!5,draw=white,line width=.8pt] (0.8750,-1.2500) rectangle ++(0.6500,-0.6500);
43 \node[text=black!45,font=\scriptsize] at (1.2000,-1.5750) {$0$};
44 \filldraw[fill=black!5,draw=white,line width=.8pt] (1.5250,-1.2500) rectangle ++(0.6500,-0.6500);
45 \node[text=black!45,font=\scriptsize] at (1.8500,-1.5750) {$0$};
46 \filldraw[fill=black!5,draw=white,line width=.8pt] (2.1750,-1.2500) rectangle ++(0.6500,-0.6500);
47 \node[text=black!45,font=\scriptsize] at (2.5000,-1.5750) {$0$};
48 \filldraw[fill=black!78,draw=white,line width=.8pt] (2.8250,-1.2500) rectangle ++(0.6500,-0.6500);
49 \node[text=white,font=\scriptsize] at (3.1500,-1.5750) {$1$};
50 \filldraw[fill=black!5,draw=white,line width=.8pt] (3.4750,-1.2500) rectangle ++(0.6500,-0.6500);
51 \node[text=black!45,font=\scriptsize] at (3.8000,-1.5750) {$0$};
52 \filldraw[fill=black!5,draw=white,line width=.8pt] (0.8750,-1.9000) rectangle ++(0.6500,-0.6500);
53 \node[text=black!45,font=\scriptsize] at (1.2000,-2.2250) {$0$};
54 \filldraw[fill=black!5,draw=white,line width=.8pt] (1.5250,-1.9000) rectangle ++(0.6500,-0.6500);
55 \node[text=black!45,font=\scriptsize] at (1.8500,-2.2250) {$0$};
56 \filldraw[fill=black!5,draw=white,line width=.8pt] (2.1750,-1.9000) rectangle ++(0.6500,-0.6500);
57 \node[text=black!45,font=\scriptsize] at (2.5000,-2.2250) {$0$};
58 \filldraw[fill=black!5,draw=white,line width=.8pt] (2.8250,-1.9000) rectangle ++(0.6500,-0.6500);
59 \node[text=black!45,font=\scriptsize] at (3.1500,-2.2250) {$0$};
60 \filldraw[fill=black!78,draw=white,line width=.8pt] (3.4750,-1.9000) rectangle ++(0.6500,-0.6500);
61 \node[text=white,font=\scriptsize] at (3.8000,-2.2250) {$1$};
62 \draw[black!60,line width=.5pt] (0.875,0.7) rectangle ++(3.25,-3.25);
63 \node[font=\scriptsize] at (1.2000,0.8900) {$0$};
64 \node[font=\scriptsize] at (1.8500,0.8900) {$1$};
65 \node[font=\scriptsize] at (2.5000,0.8900) {$2$};
66 \node[font=\scriptsize] at (3.1500,0.8900) {$3$};
67 \node[font=\scriptsize] at (3.8000,0.8900) {$4$};
68 \node[font=\scriptsize] at (0.5700,0.8900) {$k$};
69 \node[font=\small] at (2.5000,-3.0700) {unit diagonal; no entries below it};
70 \end{tikzpicture}
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