3

I'm trying to draw the following diagram in tikzcd but I want to move the marked node slightly up, is that possible to do this in tikzcd? Or is this one of the cases when it is just better to use tikz properly? I have also included a diagram from Barot's "Introduction to the Representation Theory of Algebras" that shows this. My diagram Barot's diagram

Here is my current code:

\documentclass{amsart}
\usepackage{mathtools}
\usepackage{tikz-cd}

\newcommand{\dimvec}[3]{%
  \begin{smallmatrix}#1\\#2\\#3\end{smallmatrix}%
}

\begin{document}

  \begin{tikzcd}[column sep = small]
    && \dimvec{1}{10}{100} \ar{dr} &&&&&& \dimvec{1}{01}{001} \ar{dr}\\
    & \dimvec{0}{10}{100} \ar{ur} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{1}{10}{000} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{0}{00}{010} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{1}{01}{000} \ar{dr} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{01}{001} \ar{dr} \\
    \dimvec{0}{00}{100} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{10}{000} \ar{ur} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{1}{10}{010} \ar{ur} \ar{r} \ar{dr} & \dimvec{1}{11}{010} \ar{r} & \dimvec{1}{01}{010} \ar{ur} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{0}{01}{000} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{00}{001} \\
    &&& \dimvec{0}{10}{010} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{1}{00}{000} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{01}{010} \ar{ur}
  \end{tikzcd}
\end{document}

Thank you very much in advanced for any help.

If anyone's curious the diagram is (assuming I solved my homework correctly) the Auslander-Reiten Quiver of the following quiver with relations (https://en.wikipedia.org/wiki/Quiver_(mathematics)) enter image description here

  • 2
    Welcome to TeX.SE. What is, please, your "trying code"? – Sebastiano Apr 15 '20 at 19:10
  • 1
    @Sebastiano Thank you very much for your comment, I have now included my trying code. – Najonathan Apr 15 '20 at 20:01
2

You can use yshift and want probably to \smash the shifted object in order to avoid distortions.

\documentclass{amsart}
\usepackage{mathtools}
\usepackage{tikz-cd}

\newcommand{\dimvec}[3]{%
  \begin{smallmatrix}#1\\#2\\#3\end{smallmatrix}%
}

\begin{document}

  \begin{tikzcd}[column sep = small]
    && \dimvec{1}{10}{100} \ar{dr} &&&&&& \dimvec{1}{01}{001} \ar{dr}\\
    & \dimvec{0}{10}{100} \ar{ur} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{1}{10}{000} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{0}{00}{010} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{1}{01}{000} \ar{dr} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{01}{001} \ar{dr} \\
    \dimvec{0}{00}{100} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{10}{000}
    \ar{ur} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{1}{10}{010} \ar{ur}
    \ar{r} \ar{dr} \ar[dotted, no head]{rr} & |[yshift=1.2em]| 
    \smash{\dimvec{1}{11}{010}} \ar{r} & \dimvec{1}{01}{010} \ar{ur} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{0}{01}{000} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{00}{001} \\
    &&& \dimvec{0}{10}{010} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{1}{00}{000} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{01}{010} \ar{ur}
  \end{tikzcd}
\end{document}

enter image description here

Or, as suggested by Symbol 1, with the overlay option, which will also work if you shift the node very far, and different arrow styles.

\documentclass{amsart}
\usepackage{mathtools}
\usepackage{tikz-cd}

\newcommand{\dimvec}[3]{%
  \begin{smallmatrix}#1\\#2\\#3\end{smallmatrix}%
}

\begin{document}

  \begin{tikzcd}[column sep = small,every arrow/.append
  style={-stealth,semithick}]
    && \dimvec{1}{10}{100} \ar{dr} &&&&&& \dimvec{1}{01}{001} \ar{dr}\\
    & \dimvec{0}{10}{100} \ar{ur} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{1}{10}{000} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{0}{00}{010} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{1}{01}{000} \ar{dr} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{01}{001} \ar{dr} \\
    \dimvec{0}{00}{100} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{10}{000}
    \ar{ur} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{1}{10}{010} \ar{ur}
    \ar{r} \ar{dr} \ar[dotted, no head]{rr} & |[yshift=1.2em,overlay]| 
    \dimvec{1}{11}{010} \ar{r} & \dimvec{1}{01}{010} \ar{ur} \ar{dr} \ar[dotted, no head]{rr} && \dimvec{0}{01}{000} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{00}{001} \\
    &&& \dimvec{0}{10}{010} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{1}{00}{000} \ar{ur} \ar[dotted, no head]{rr} && \dimvec{0}{01}{010} \ar{ur}
  \end{tikzcd}
\end{document}

enter image description here

  • 1
    maybe overlay in place of \smash? Because I like to go full-TikZ. – Symbol 1 Apr 15 '20 at 20:46
  • @Symbol1 Yes, that's a great suggestion. Do you understand the logic about this diagram? It almost seems that these integers are coordinates but but not quite. – user194703 Apr 15 '20 at 20:49
  • 1
    So OP mentioned a book Introduction to the Representation Theory of Algebras and the figure is found on page 131. From what I have learned, each node is a representation of a quiver. Each arrow is some interesting morphism between representations. And by a representation of a quiver I mean it gives vertices in the quiver a dimension (0 or 1). In OP's case, the quiver is (7.3) in the book... That's all I can tell. – Symbol 1 Apr 15 '20 at 21:03
  • 1
    @Schrödinger's cat Thank you very much for the answer! To answer your question regarding the diagram, the nodes are equivalence classes of indecomposable modules of path algebra of a quiver. The nodes are called dimension vectors of the modules, which are written in the shape of the original quiver. The arrows are irreducible morphism between them. This new quiver is called the Auslander-Reiten quiver of the path algebra (en.wikipedia.org/wiki/Auslander%E2%80%93Reiten_theory). – Najonathan Apr 15 '20 at 22:10

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