  The box-ball system is studied from the viewpoint of combinatorics of words
and tableaux. Each state of the box-ball system can be transformed into a pair
of tableaux $(P,Q)$ by the Robinson-Schensted-Knuth correspondence. In the
language of tableaux, the $P$-symbol gives rise to a conserved quantity of the
box-ball system, and the $Q$-symbol evolves independently of the $P$-symbol.
The time evolution of the $Q$-symbol is described explicitly in terms of the
box-labels.
