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For standard Young tableaux, semistandard Young tableaux, and other related two-dimensional arrays of numbers like plane partitions. Including their combinatorial theory and their application in representation theory and algebraic geometry.
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Combine two types of permutations in a Young diagram?
Given a Young diagram $Y$, for each row $R$ choose a permutation $\sigma_R$ of $\{1,\dots, |R|\}$, where $|R|$ is the size of row $R$. Let $\sigma_R(i)$ be the “row coordinate” of the $i$th cell in ro …