I just computed the Young tableaux of partition $3+1+1$ for the conjugacy classes of $S_5$. It would be nice if anyone could confirm it's correctness. Thanks.
2026-03-29 12:37:32.1774787852
Young tableaux of partition $3+1+1$ for the conjugacy classes of $S_5$
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Yes, it's correct. Note that you only need to generate the first row. The first column needs to be strictly increasing and thus follows immediately. So your first row should be indeed 123, 124, 125, 134, 135, 145 (in what I consider to be a more orderly fashion).