Name
Abstract | ||
|---|---|---|
We prove a converse to Myhill's "Garden-of-Eden" theorem and obtain in this manner a characterization of amenability in terms of cellular automata: A group G is amenable if and only if every cellular automaton with carrier G that has gardens of Eden also has mutually erasable patterns. This answers a question by Schupp, and solves a conjecture by Ceccherini-Silberstein, Machi and Scarabotti. Furthermore, for non-amenable G the cellular automaton with carrier G that has gardens of Eden but no mutually erasable patterns may also be assumed to be linear. An appendix by Dawid Kielak shows that group rings without zero divisors are Ore domains precisely when the group is amenable, answering a conjecture attributed to Guba. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.4171/JEMS/900 | JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY |
Keywords | Field | DocType |
Cellular automata,Moore-Myhill theorem,amenability of groups,Ore domains,localization | Cellular automaton,Discrete mathematics,Group rings,Converse,Combinatorics,Zero divisor,If and only if,Conjecture,Mathematics | Journal |
Volume | Issue | ISSN |
21 | 10 | 1435-9855 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Bartholdi | 1 | 27 | 8.74 |
| Dawid Kielak | 2 | 0 | 0.68 |