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My try was:

sage: joinme = ( lambda x,y:    y.contains(x) )
sage: p = Poset( ( [ b for n in [1..5] for b in Partitions(n) ], joinme ) )
sage: p . show()
Launched png viewer for Graphics object consisting of 44 graphics primitives
sage: latex( p )

The png file shows immediately.

And the latex conversion of p requires tikzpicture. We get the code, if we really need to make latex work with it.

\begin{tikzpicture}
%
\useasboundingbox (0,0) rectangle (5.0cm,5.0cm);
%
\definecolor{cv0}{rgb}{0.0,0.0,0.0}
\definecolor{cfv0}{rgb}{1.0,1.0,1.0}
\definecolor{clv0}{rgb}{0.0,0.0,0.0}
...  many further lines ...
\raisebox{-.6ex}{$\begin{array}[b]{*{5}c}\cline{1-5}
\lr{\phantom{x}}&\lr{\phantom{x}}&\lr{\phantom{x}}&\lr{\phantom{x}}&\lr{\phantom{x}}\\\cline{1-5}
\end{array}$}
}$},x=5.0cm,y=0.7357cm]{v17}
%
\Edge[lw=0.1cm,style={post, bend right,color=cv0v1,},](v0)(v1)
\Edge[lw=0.1cm,style={post, bend right,color=cv0v5,},](v0)(v5)
\Edge[lw=0.1cm,style={post, bend right,color=cv1v2,},](v1)(v2)
\Edge[lw=0.1cm,style={post, bend right,color=cv1v6,},](v1)(v6)
\Edge[lw=0.1cm,style={post, bend right,color=cv2v3,},](v2)(v3)
\Edge[lw=0.1cm,style={post, bend right,color=cv2v7,},](v2)(v7)
\Edge[lw=0.1cm,style={post, bend right,color=cv3v4,},](v3)(v4)
\Edge[lw=0.1cm,style={post, bend right,color=cv3v8,},](v3)(v8)
\Edge[lw=0.1cm,style={post, bend right,color=cv5v6,},](v5)(v6)
\Edge[lw=0.1cm,style={post, bend right,color=cv5v11,},](v5)(v11)
\Edge[lw=0.1cm,style={post, bend right,color=cv6v7,},](v6)(v7)
\Edge[lw=0.1cm,style={post, bend right,color=cv6v9,},](v6)(v9)
\Edge[lw=0.1cm,style={post, bend right,color=cv6v12,},](v6)(v12)
\Edge[lw=0.1cm,style={post, bend right,color=cv7v8,},](v7)(v8)
\Edge[lw=0.1cm,style={post, bend right,color=cv7v10,},](v7)(v10)
\Edge[lw=0.1cm,style={post, bend right,color=cv7v13,},](v7)(v13)
\Edge[lw=0.1cm,style={post, bend right,color=cv9v10,},](v9)(v10)
\Edge[lw=0.1cm,style={post, bend right,color=cv9v14,},](v9)(v14)
\Edge[lw=0.1cm,style={post, bend right,color=cv11v12,},](v11)(v12)
\Edge[lw=0.1cm,style={post, bend right,color=cv11v15,},](v11)(v15)
\Edge[lw=0.1cm,style={post, bend right,color=cv12v13,},](v12)(v13)
\Edge[lw=0.1cm,style={post, bend right,color=cv12v14,},](v12)(v14)
\Edge[lw=0.1cm,style={post, bend right,color=cv12v16,},](v12)(v16)
\Edge[lw=0.1cm,style={post, bend right,color=cv15v16,},](v15)(v16)
\Edge[lw=0.1cm,style={post, bend right,color=cv15v17,},](v15)(v17)
%
\end{tikzpicture}