A1 Refereed original research article in a scientific journal
Trees are Nilrigid
Authors: Salo, Ville
Publisher: Old City Publishing
Publication year: 2026
Journal: Journal of Cellular Automata
Volume: 18
Issue: 4-5
First page : 245
Last page: 256
ISSN: 1557-5969
eISSN: 1557-5977
DOI: https://doi.org/10.32908/jca.v18.200325
Publication's open availability at the time of reporting: No Open Access
Publication channel's open availability : No Open Access publication channel
Web address : https://www.oldcitypublishing.com/journals/jca-home/jca-issue-contents/jca-volume-18-number-4-5-2026/jca-18-4-5-p-245-256/
We study cellular automata (CA) on the unoriented 𝑘-regular tree 𝑇𝑘, i.e. continuous maps acting on vertex-labelings of 𝑇𝑘 which commute with all automorphisms of the tree.We prove that every CA that is asymptotically nilpotent, meaning every configuration converges to the same constant configuration, is nilpotent, meaning each configuration is mapped to that configuration after finite time.
Keywords: Cellular automata, dynamical systems, Nilpotency, trees, group actions, free groups
Funding information in the publication:
Research supported by the Academy of Finland grant 2608073211.
