08_prime_forests.tex

Paper X: Universal Residual Seeds and Conditional Occupied-System Completion

08_prime_forests.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center] at (3,4.4) {$p=2$};
4 \node[font=\small,align=center] at (5.05,4.4) {$p=3$};
5 \node[font=\small,align=center] at (7.1,4.4) {$p=5$};
6 \node[font=\small,align=center] at (9.15,4.4) {$p=7$};
7 \node[font=\small,align=center] at (11.2,4.4) {$p=13$};
8 \node[font=\small,align=center,anchor=east] at (1.4,3.5) {$m=1$};
9 \path[draw=black!35,fill=black!12] (2.2,3.05) rectangle (3.8,3.9);
10 \node[font=\small,align=center] at (3,3.48) {$1$};
11 \path[draw=black!35,fill=white] (4.25,3.05) rectangle (5.85,3.9);
12 \node[font=\small,align=center] at (5.05,3.48) {$0$};
13 \path[draw=black!35,fill=black!12] (6.3,3.05) rectangle (7.9,3.9);
14 \node[font=\small,align=center] at (7.1,3.48) {$2$};
15 \path[draw=black!35,fill=white] (8.35,3.05) rectangle (9.95,3.9);
16 \node[font=\small,align=center] at (9.15,3.48) {$0$};
17 \path[draw=black!35,fill=black!12] (10.4,3.05) rectangle (12,3.9);
18 \node[font=\small,align=center] at (11.2,3.48) {$2$};
19 \node[font=\small,align=center,anchor=east] at (1.4,2.5) {$m=2$};
20 \path[draw=black!35,fill=white] (2.2,2.05) rectangle (3.8,2.9);
21 \node[font=\small,align=center] at (3,2.48) {$0$};
22 \path[draw=black!35,fill=white] (4.25,2.05) rectangle (5.85,2.9);
23 \node[font=\small,align=center] at (5.05,2.48) {$0$};
24 \path[draw=black!35,fill=black!12] (6.3,2.05) rectangle (7.9,2.9);
25 \node[font=\small,align=center] at (7.1,2.48) {$2$};
26 \path[draw=black!35,fill=white] (8.35,2.05) rectangle (9.95,2.9);
27 \node[font=\small,align=center] at (9.15,2.48) {$0$};
28 \path[draw=black!35,fill=black!12] (10.4,2.05) rectangle (12,2.9);
29 \node[font=\small,align=center] at (11.2,2.48) {$2$};
30 \node[font=\small,align=center,anchor=east] at (1.4,1.5) {$m=3$};
31 \path[draw=black!35,fill=white] (2.2,1.05) rectangle (3.8,1.9);
32 \node[font=\small,align=center] at (3,1.48) {$0$};
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34 \node[font=\small,align=center] at (5.05,1.48) {$0$};
35 \path[draw=black!35,fill=black!12] (6.3,1.05) rectangle (7.9,1.9);
36 \node[font=\small,align=center] at (7.1,1.48) {$2$};
37 \path[draw=black!35,fill=white] (8.35,1.05) rectangle (9.95,1.9);
38 \node[font=\small,align=center] at (9.15,1.48) {$0$};
39 \path[draw=black!35,fill=black!12] (10.4,1.05) rectangle (12,1.9);
40 \node[font=\small,align=center] at (11.2,1.48) {$2$};
41 \node[font=\small,align=center,font=\footnotesize] at (7,0.15) {Counts of $x\in\mathbb Z/p^m\mathbb Z$ with $x^2+1=0$.};
42 \end{tikzpicture}

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