Layout of three Young diagram

I am trying to let these three diagrams more neat. Like, (1,1,1),(2,1),(3) are lying on the same line, and the arrows all point the middle of Young diagram. Anyone could help me?

My code is:

Example: Partition of 3

\begin{multicols}{3}
\noindent
$(1,1,1)\longleftrightarrow$ $\begin{Young} \cr \cr \cr \end{Young}$
$(2,1)\longleftrightarrow$ $\begin{Young} &\cr \cr \end{Young}$
$(3)\longleftrightarrow$ $\begin{Young} &&\cr \end{Young}$
\end{multicols}

• Welcome to TeX.SX! Please help us (and also you) and add a minimal working example (MWE), that illustrates your problem. Reproducing the problem and finding out what the issue is will be much easier when we see compilable code, starting with \documentclass and ending with \end{document}. – Bobyandbob Jul 12 '18 at 14:27

If you would consider using a different package for your Young diagrams, namely youngtab, the vertical centering of the diagrams on the line is easy. You just need to load the package with the vcentermath option.
The slightly jumbled appearance you show come from using the multicols environment. I don't know why you have that, seems to me that a single display math environment ($...$) makes more sense here.
\documentclass{article}
$(1,1,1)\longleftrightarrow\; \yng(1,1,1)\qquad (2,1)\longleftrightarrow\; \yng(2,1)\qquad (3)\longleftrightarrow\; \yng(3)$