i have the following definition of a young tableau: A Young tableau is an m × n matrix ($t_{i,j}$) with entries from N ∪ {∞}, for which it holds that in each row and each column the values ascend from left to right and from top to bottom, respectively. The entries with value ∞ stand for empty places.
Task: Specify a 3 × 3 Young tableau with entries 4, 16, 7, 1, 9.
Here is my Solution: $$\begin{array} {|r|r|}\hline 1 & 4 & 7 \\ \hline 9 & 16 & ∞ \\ \hline ∞ & ∞ & ∞ \\ \hline \end{array}$$ but im not sure, if it should look like this:
$$\begin{array} {|r|r|}\hline 1 & 4 & 7 \\ \hline 4 & 7 & 9 \\ \hline 7 & 9 & 16 \\ \hline \end{array}$$
based on the given description, both could be possible. But after i looked up the wikipedia article, it seems that it is not common for such a tableau to hold two numbers with the same value. Therefore I think solution 1 is the correct one.
So I'm quite confused. Maybe someone can give me a hint.
Thank you :)
