Different Directed graph

Question

I need to do a graph similar to the one in the picture above but I don't know how to do the horizontal lines without the arrow, or the vertical arrow. The best I could do is the following:

\documentclass{amsart}
\usepackage{tikz} 
\begin{document}
\begin{center}
\begin{tikzpicture}
    \node (p1) at ( 0, 0) {}; 
    \node (p2) at ( 1, -0.2) {i};
    \node (p3) at ( 3,0) {};
    \node (p4) at ( 0,1) {};
    \node (p5) at ( 2,1.2) {n+j};
    \node (p6) at ( 3,1) {};
    \begin{scope}[every path/.style={->}]
       \draw (p1) -- (p3); 
       \draw (p4) -- (p6);
       \draw (p2) -- (p5);
    \end{scope}  
\end{tikzpicture}
\end{center}
\end{document}

Output

Answer 1

Is this the desired result:

Notes:

• If you don't want arrow heads on the end of lines, either change the style to every path/.style={-} or simply eliminate that option as I have done below. Lines do not get arrow heads be default.
• The style of the arrow that you desire is -latex. So, just add that option when needed (as is the case for the orange line).
• Added shorten <= and shorten >= to extend the orange line. Alternatively you could manully select points that are on the line.
• The calc library was used to compute the midway coordinates with which the vertical black line was drawn.
• I made the node labels to be in math mode by adding the $.
• Colors added to make it easier to know which drawing command is doing what.

Code:

\documentclass{amsart}
\usepackage{tikz} 
\usetikzlibrary{calc}
\begin{document}
\begin{center}
\begin{tikzpicture}[thick]
    \node (p1) at ( 0, 0) {}; 
    \node (p2) at ( 1, -0.2) {$i$};
    \node (p3) at ( 3,0) {};
    \node (p4) at ( 0,1) {};
    \node (p5) at ( 2,1.2) {$n+j$};
    \node (p6) at ( 3,1) {};
    \coordinate (p1MidwayP3) at ($(p1)!0.5!(p3)$);
    \coordinate (p4MidwayP6) at ($(p4)!0.5!(p6)$);
    \begin{scope}%[every path/.style={-}]
       \draw [red] (p1) -- (p3); 
       \draw [blue] (p4) -- (p6);
       \draw [orange, shorten <=-0.08cm, shorten >=-0.10cm, -latex](p2) -- (p5);
       \draw  (p1MidwayP3) -- (p4MidwayP6);
    \end{scope}  
\end{tikzpicture}
\end{center}
\end{document}

Answer 2

A PSTricks solution, combined with xfp:

\documentclass{article}

\usepackage{pstricks-add}
\usepackage{xfp}

\begin{document}

\def\Horizontal{5} % length of the horizontal line segments
\def\Vertical{3}   % length of the vertical   line segment
\def\Indent{0.5}   % indentation of the arrow from both sides
\begin{pspicture}(0,-0.4)(\Horizontal,\fpeval{\Vertical+0.45})
  \psline(0,0)(\Horizontal,0)
  \psline(0,\Vertical)(\Horizontal,\Vertical)
  \psline(\fpeval{\Horizontal/2},0)(\fpeval{\Horizontal/2},\Vertical)
  \psline{->}(\Indent,0)(\fpeval{\Horizontal-\Indent},\Vertical)
  \uput[270](\Indent,0){$i$}
  \uput[90](\fpeval{\Horizontal-\Indent},\Vertical){$n+j$}
\end{pspicture}

\end{document}

All you have to do is choose the values of \Horizontal, \Vertical, and \Indent and the drawing will be adjusted accordingly.