Geodesic
Box-ball systems and Robinson-Schensted-Knuth correspondence
Journal of Algebraic Combinatorics, Tome 19 (2004) no. 1, pp. 67-89.

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Summary: We study a box-ball system 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.
Keywords: box-ball system, Robinson-Schensted-knuth correspondence, soliton cellular automaton, Young tableau, knuth equivalence 
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     title = {Box-ball systems and {Robinson-Schensted-Knuth} correspondence},
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Fukuda, Kaori. Box-ball systems and Robinson-Schensted-Knuth correspondence. Journal of Algebraic Combinatorics, Tome 19 (2004) no. 1, pp. 67-89. http://geodesic.mathdoc.fr/item/JAC_2004__19_1_a1/