Diagrams for https://math.stackexchange.com/a/2371961/116766

Diag1.svg

Diag1.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{tikz}
\begin{document}
  \begin{tikzpicture}[domain=0:5]
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    \draw[very thin,color=gray] (-0.1,-0.1) grid (4.9,3.9);
    \draw[->] (-0.2,0) -- (5.1,0);
    \draw[->] (0,-0.2) -- (0,4.1);
    \filldraw[black] (0,3) circle (2pt);
    \filldraw[black] (3,1) circle (2pt);
    \filldraw[black] (4,0) circle (2pt);
    \draw[dashed] (0,3) -- (4,0);
  \end{tikzpicture}
\end{document}

Diag2.svg

Diag2.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{tikz-cd}
\begin{document}
  \begin{tikzpicture}[domain=0:2]
    \path[fill=gray!20] (0,1) -- (1,0) -- (1.9,0) -- (1.9,3.9) -- (0,3.9) -- (0,1); 
    \draw[very thin,color=gray] (-0.1,-0.1) grid (1.9,3.9);
    \draw[-cm to] (-0.2,0) -- (2.1,0);
    \draw[-cm to] (0,-0.2) -- (0,4.1);
    \filldraw[black] (1,1) circle (2pt);
    \filldraw[black] (1,0) circle (2pt);
    \filldraw[black] (0,3) circle (2pt);
    \filldraw[black] (0,2) circle (2pt);
    \filldraw[black] (0,1) circle (2pt);
    \draw[dashed] (0,1) -- (1,0);
  \end{tikzpicture}
\end{document}

Diag3.svg

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Diag3.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{tikz-cd}
\begin{document}
  \begin{tikzpicture}[domain=0:3]
    \path[fill=gray!20] (0,1) -- (2,0) -- (2.9,0) -- (2.9,3.9) -- (0,3.9) -- (0,1); 
    \draw[very thin,color=gray] (-0.1,-0.1) grid (2.9,3.9);
    \draw[-cm to] (-0.2,0) -- (3.1,0);
    \draw[-cm to] (0,-0.2) -- (0,4.1);
    \filldraw[black] (2,3) circle (2pt);
    \filldraw[black] (2,2) circle (2pt);
    \filldraw[black] (2,1) circle (2pt);
    \filldraw[black] (2,0) circle (2pt);
    \filldraw[black] (1,2) circle (2pt);
    \filldraw[black] (1,1) circle (2pt);
    \filldraw[black] (0,1) circle (2pt);
    \draw[dashed] (0,1) -- (2,0);
  \end{tikzpicture}
\end{document}

Diag4.svg

Diag4.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{tikz-cd}
\begin{document}
  \begin{tikzpicture}[domain=0:7]
    \path[fill=gray!20] (0,1) -- (1,0) -- (6.9,0) -- (6.9,3.9) -- (0,3.9) -- (0,1); 
    \draw[very thin,color=gray] (-0.1,-0.1) grid (6.9,3.9);
    \draw[-cm to] (-0.2,0) -- (7.1,0);
    \draw[-cm to] (0,-0.2) -- (0,4.1);
    \filldraw[black] (6,3) circle (2pt);
    \filldraw[black] (6,2) circle (2pt);
    \filldraw[black] (6,1) circle (2pt);
    \filldraw[black] (6,0) circle (2pt);
    \filldraw[black] (4,2) circle (2pt);
    \filldraw[black] (4,1) circle (2pt);
    \filldraw[black] (4,0) circle (2pt);
    \filldraw[black] (3,2) circle (2pt);
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    \filldraw[black] (2,1) circle (2pt);
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    \filldraw[black] (1,1) circle (2pt);
    \filldraw[black] (1,0) circle (2pt);
    \filldraw[black] (0,1) circle (2pt);
    \draw[dashed] (0,1) -- (1,0);
  \end{tikzpicture}
\end{document}