= Triangular vanishing of Young-symmetrizer products
{title2=$t>u\Longrightarrow h_th_u=0$}
For <standard tableaux> of the same shape and $h_t=c_tr_t$, $t>u$ in <column-reading order of standard Young tableaux> implies $h_th_u=0$. If there were no row-column collision, each column of $u$ would select one entry from each eligible row of $t$. Its sorted first column is componentwise at least the row minima of $t$; equality fixes those selected entries and permits induction after deleting the column. Thus no collision implies $u\geq t$. A collision gives $r_tc_u=0$.
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