  We realise the Benkart-Sottile-Stroomer switching involution on ballot
tableau pairs of partition shape as a recursive internal row insertion
procedure. The key observation needed to establish such realisation is that
internal row insertion operations are Knuth commutative. In fact, the Knuth
class of a word encoding the sequence of internal row insertion operations
preserves the $P$-tableau in the Sagan-Stanley skew RSK correspondence when the
matrix word is empty. It confirms that all Littlewood-Richardson (LR)
commutors, known up to date, are involutions and coincide as predicted by Pak
and Vallejo.
