Box-ball systems and Robinson-Schensted-Knuth correspondence
arXiv:math/0105226
Abstract
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 by the Robinson-Schensted-Knuth correspondence. In the language of tableaux, the -symbol gives rise to a conserved quantity of the box-ball system, and the -symbol evolves independently of the -symbol. The time evolution of the -symbol is described explicitly in terms of the box-labels.
25 pages; We revised the paper vastly. The construction of the theory is also modified