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

Diag1.svg

<?xml version="1.0" encoding="UTF-8"?>
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="209pt" height="170pt" viewBox="0 0 209 170" version="1.1">
<defs>
<clipPath id="clip1">
  <path d="M 7 0 L 9 0 L 9 169.660156 L 7 169.660156 Z M 7 0 "/>
</clipPath>
<clipPath id="clip2">
  <path d="M 155 151 L 177 151 L 177 169.660156 L 155 169.660156 Z M 155 151 "/>
</clipPath>
<clipPath id="clip3">
  <path d="M 0 35 L 174 35 L 174 169.660156 L 0 169.660156 Z M 0 35 "/>
</clipPath>
</defs>
<g id="surface1">
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(89.99939%,89.99939%,89.99939%);fill-opacity:1;" d="M 8.273438 43.644531 L 165.601562 161.636719 L 200.996094 161.636719 L 200.996094 8.246094 L 8.273438 8.246094 L 8.273438 43.644531 "/>
<path style="fill:none;stroke-width:0.19925;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(50%,50%,50%);stroke-opacity:1;stroke-miterlimit:10;" d="M -2.833532 0.000986126 L 138.897887 0.000986126 M -2.833532 28.345581 L 138.897887 28.345581 M -2.833532 56.692991 L 138.897887 56.692991 M -2.833532 85.040401 L 138.897887 85.040401 M -0.00132432 -2.834036 L -0.00132432 110.552788 M 28.346086 -2.834036 L 28.346086 110.552788 M 56.693495 -2.834036 L 56.693495 110.552788 M 85.040905 -2.834036 L 85.040905 110.552788 M 113.388315 -2.834036 L 113.388315 110.552788 " transform="matrix(1.3875,0,0,-1.3875,8.275275,161.638087)"/>
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -5.668554 0.000986126 L 144.111851 0.000986126 " transform="matrix(1.3875,0,0,-1.3875,8.275275,161.638087)"/>
<path style="fill:none;stroke-width:0.31879;stroke-linecap:round;stroke-linejoin:round;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -1.195234 1.594455 C -1.096698 0.997608 0.00127477 0.0995222 0.299698 0.000986126 C 0.00127477 -0.100365 -1.096698 -0.995635 -1.195234 -1.595298 " transform="matrix(1.3875,0,0,-1.3875,208.2287,161.638087)"/>
<g clip-path="url(#clip1)" clip-rule="nonzero">
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -0.00132432 -5.669059 L -0.00132432 115.763937 " transform="matrix(1.3875,0,0,-1.3875,8.275275,161.638087)"/>
</g>
<path style="fill:none;stroke-width:0.31879;stroke-linecap:round;stroke-linejoin:round;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M -1.196383 1.594793 C -1.095032 0.995131 0.000126126 0.0998604 0.29855 0.00132432 C 0.000126126 -0.100027 -1.095032 -0.995297 -1.196383 -1.594959 " transform="matrix(0,-1.3875,-1.3875,0,8.275275,1.0158)"/>
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 1.991919 85.040401 C 1.991919 86.141189 1.099464 87.033644 -0.00132432 87.033644 C -1.099297 87.033644 -1.991752 86.141189 -1.991752 85.040401 C -1.991752 83.939612 -1.099297 83.047157 -0.00132432 83.047157 C 1.099464 83.047157 1.991919 83.939612 1.991919 85.040401 Z M 1.991919 85.040401 " transform="matrix(1.3875,0,0,-1.3875,8.275275,161.638087)"/>
<path style="fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 87.034149 28.345581 C 87.034149 29.446369 86.141694 30.338824 85.040905 30.338824 C 83.940117 30.338824 83.047662 29.446369 83.047662 28.345581 C 83.047662 27.247608 83.940117 26.355153 85.040905 26.355153 C 86.141694 26.355153 87.034149 27.247608 87.034149 28.345581 Z M 87.034149 28.345581 " transform="matrix(1.3875,0,0,-1.3875,8.275275,161.638087)"/>
<path style=" stroke:none;fill-rule:nonzero;fill:rgb(0%,0%,0%);fill-opacity:1;" d="M 168.363281 161.636719 C 168.363281 160.109375 167.128906 158.875 165.601562 158.875 C 164.074219 158.875 162.835938 160.109375 162.835938 161.636719 C 162.835938 163.164062 164.074219 164.402344 165.601562 164.402344 C 167.128906 164.402344 168.363281 163.164062 168.363281 161.636719 Z M 168.363281 161.636719 "/>
<g clip-path="url(#clip2)" clip-rule="nonzero">
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-miterlimit:10;" d="M 115.378743 0.000986126 C 115.378743 1.101774 114.489104 1.991414 113.388315 1.991414 C 112.287527 1.991414 111.395072 1.101774 111.395072 0.000986126 C 111.395072 -1.099802 112.287527 -1.992257 113.388315 -1.992257 C 114.489104 -1.992257 115.378743 -1.099802 115.378743 0.000986126 Z M 115.378743 0.000986126 " transform="matrix(1.3875,0,0,-1.3875,8.275275,161.638087)"/>
</g>
<g clip-path="url(#clip3)" clip-rule="nonzero">
<path style="fill:none;stroke-width:0.3985;stroke-linecap:butt;stroke-linejoin:miter;stroke:rgb(0%,0%,0%);stroke-opacity:1;stroke-dasharray:2.98883,2.98883;stroke-miterlimit:10;" d="M -0.00132432 85.040401 L 113.388315 0.000986126 " transform="matrix(1.3875,0,0,-1.3875,8.275275,161.638087)"/>
</g>
</g>
</svg>

Diag1.tex

\documentclass[12pt]{article}
\usepackage{stix}
\usepackage{tikz}
\begin{document}
  \begin{tikzpicture}[domain=0:5]
    \path[fill=gray!20] (0,3) -- (4,0) -- (4.9,0) -- (4.9,3.9) -- (0,3.9) -- (0,3); 
    \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

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);
    \filldraw[black] (3,1) circle (2pt);
    \filldraw[black] (3,0) circle (2pt);
    \filldraw[black] (2,1) circle (2pt);
    \filldraw[black] (2,0) circle (2pt);
    \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}