Paper IV: Cyclic Analytic Functions, Reciprocal Families, and Spectral Zero Data

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round,line join=round]
2 \node[font=\sffamily\footnotesize] at (2.15000,4.00000) {three singletons};
3 \draw[fill=black!12,draw=black!40,line width=.35pt] (0.45000,2.45000) rectangle ++(0.66000,0.75000);
4 \draw[fill=black] (0.78000,2.82000) circle (0.085);
5 \draw[fill=black!12,draw=black!40,line width=.35pt] (1.27000,2.45000) rectangle ++(0.66000,0.75000);
6 \draw[fill=black] (1.60000,2.82000) circle (0.085);
7 \draw[fill=black!12,draw=black!40,line width=.35pt] (2.09000,2.45000) rectangle ++(0.66000,0.75000);
8 \draw[fill=black] (2.42000,2.82000) circle (0.085);
9 \node[] at (2.15000,1.40000) {$r^3\kappa_1^3$};
10 \node[] at (2.15000,0.40000) {$15r^3$};
11 \node[font=\sffamily\footnotesize] at (6.50000,4.00000) {one pair, one singleton};
12 \draw[fill=black!12,draw=black!40,line width=.35pt] (4.80000,2.45000) rectangle ++(1.32000,0.75000);
13 \draw[fill=black] (5.13000,2.82000) circle (0.085);
14 \draw[fill=black] (5.79000,2.82000) circle (0.085);
15 \draw[fill=black!12,draw=black!40,line width=.35pt] (6.28000,2.45000) rectangle ++(0.66000,0.75000);
16 \draw[fill=black] (6.61000,2.82000) circle (0.085);
17 \node[] at (6.50000,1.40000) {$3r^2\kappa_1\kappa_2$};
18 \node[] at (6.50000,0.40000) {$30r^2$};
19 \node[font=\sffamily\footnotesize] at (10.85000,4.00000) {one triple};
20 \draw[fill=black!12,draw=black!40,line width=.35pt] (9.15000,2.45000) rectangle ++(1.98000,0.75000);
21 \draw[fill=black] (9.48000,2.82000) circle (0.085);
22 \draw[fill=black] (10.14000,2.82000) circle (0.085);
23 \draw[fill=black] (10.80000,2.82000) circle (0.085);
24 \node[] at (10.85000,1.40000) {$2r\kappa_3$};
25 \node[] at (10.85000,0.40000) {$16r$};
26 \node[] at (6.50000,-0.50000) {$P_{2,3}(r)=\frac{6!}{3!}\,B_3(r\kappa_1,r\kappa_2,2r\kappa_3)$};
27 \end{tikzpicture}

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