= Content vector of a standard Young tableau
{title2=$c_T$}
= Content vectors of standard Young tableaux
{synonym}
The content vector of a <standard Young tableau> $T$ is $(c_T(1),\ldots,c_T(n))$, where $c_T(r)$ is the <Content of a Young-diagram cell> containing $r$. Such vectors are exactly the integer vectors satisfying: the first coordinate is zero; each subsequent coordinate has an earlier neighbor differing by one; between two occurrences of $a$ both $a-1$ and $a+1$ occur. To reconstruct the tableau, insert each entry in the next available cell on its prescribed diagonal. The neighbor conditions supply its required predecessors, so each insertion is an <addable node of a Young diagram>.
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