Soliton cellular automata associated with infinite reduced words

Max Glick, Rei Inoue, Pavlo Pylyavskyy

Research output: Contribution to journalArticlepeer-review


We consider a family of cellular automata φn; k/ associated with infinite reduced elements on the affine symmetric group Ŝn, which is a tropicalization of the rational maps introduced in [3]. We study the soliton solutions for φn; k/ and explore a duality with the sln-box-ball system.

Original languageEnglish (US)
Pages (from-to)249-302
Number of pages54
JournalAnnales de l'Institut Henri Poincare (D) Combinatorics, Physics and their Interactions
Issue number2
StatePublished - 2020

Bibliographical note

Funding Information:
1 Rei Inoue was partially supported by JSPS KAKENHI Grant Number 26400037 and 16H03927. 2 Pavlo Pylyavskyy was partially supported by NSF grants DMS-1148634, DMS-1351590, and Sloan Fellowship.

Publisher Copyright:
© European Mathematical Society.


  • Affine symmetric group
  • Box-ball system
  • Tropical solitons


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