**Séminaire Lotharingien de Combinatoire (2021)**

Sém. Lothar. Combin.85B(2021), Art. 14, 12 pp.

**Proceedings of the 33rd Conference on Formal Power****Series and Algebraic Combinatorics ****Ben Drucker, Eli Garcia, Emily Gunawan, and Rose Silver**

A box-ball system is a collection of discrete time states representing a permutation,

on which there is an action called a BBS move. After a finite number of BBS moves

the system decomposes into a collection of soliton states; these are weakly

increasing and invariant under BBS moves. The students proved that when this

collection of soliton states is a Young tableau or coincides with a partition of a type

described by Robinson-Schensted (RS), then it is an RS insertion tableau. They also

studied the number of steps required to reach this state.