Admissible adjacent swap of a standard Young tableau
= Admissible adjacent swap of a standard Young tableau
{title2=$s_iT,\quad |c_T(i+1)-c_T(i)|>1$}
Swapping consecutive labels $i,i+1$ preserves a <standard Young tableau> exactly when their cells are incomparable in the row-and-column order. Their contents then differ by more than one in absolute value. These admissible swaps connect all standard tableaux of any fixed shape, as adjacent swaps connect <linear extensions of a partially ordered set>.