Box-Ball Systems and Robinson-Schensted-Knuth Correspondence

Authors:
Kaori Fukuda
Affiliations:
Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan. fukuda@math.kobe-u.ac.jp
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2004

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Abstract

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.