Oscillating path in the Young lattice
= Oscillating path in the Young lattice
= Oscillating tableau
{synonym}
An oscillating tableau is a sequence of <Young diagrams>, each obtained from its predecessor by adding or removing one box. These are paths in the <Young branching graph> with both directions allowed. A path of length $\ell$ from the empty diagram to $\lambda\vdash n$, with $\ell-n=2m\geq0$, has count $\ell!f_\lambda/(2^m n!m!)$. This differs from a saturated upward path, whose length must equal $n$.