| Field |
Value |
Language |
|
dc.contributor.author |
Berdinsky, D |
|
|
dc.contributor.author |
Elder, M
https://orcid.org/0000-0002-2438-3945
|
|
|
dc.contributor.author |
Taback, J |
|
|
dc.date.accessioned |
2022-03-20T00:21:00Z |
|
|
dc.date.available |
2022-03-20T00:21:00Z |
|
|
dc.identifier.citation |
International Journal of Algebra and Computation, pp. 1-27 |
|
|
dc.identifier.issn |
0218-1967 |
|
|
dc.identifier.issn |
1793-6500 |
|
|
dc.identifier.uri |
http://hdl.handle.net/10453/155380
|
|
|
dc.description.abstract |
<jats:p> In contrast to being automatic, being Cayley automatic a priori has no geometric consequences. Specifically, Cayley graphs of automatic groups enjoy a fellow traveler property. Here, we study a distance function introduced by the first author and Trakuldit which aims to measure how far a Cayley automatic group is from being automatic, in terms of how badly the Cayley graph fails the fellow traveler property. The first author and Trakuldit showed that if it fails by at most a constant amount, then the group is in fact automatic. In this paper, we show that for a large class of non-automatic Cayley automatic groups this function is bounded below by a linear function in a precise sense defined herein. In fact, for all Cayley automatic groups which have super-quadratic Dehn function, or which are not finitely presented, we can construct a non-decreasing function which (1) depends only on the group and (2) bounds from below the distance function for any Cayley automatic structure on the group. </jats:p> |
|
|
dc.language |
en |
|
|
dc.publisher |
World Scientific Pub Co Pte Ltd |
|
|
dc.relation |
http://purl.org/au-research/grants/arc/DP160100486
|
|
|
dc.relation.ispartof |
International Journal of Algebra and Computation |
|
|
dc.relation.isbasedon |
10.1142/s0218196722500199 |
|
|
dc.rights |
info:eu-repo/semantics/embargoedAccess |
|
|
dc.subject |
0101 Pure Mathematics, 0103 Numerical and Computational Mathematics, 0802 Computation Theory and Mathematics |
|
|
dc.subject.classification |
General Mathematics |
|
|
dc.title |
On the geometry of Cayley automatic groups |
|
|
dc.type |
Journal Article |
|
|
utslib.for |
0101 Pure Mathematics |
|
|
utslib.for |
0103 Numerical and Computational Mathematics |
|
|
utslib.for |
0802 Computation Theory and Mathematics |
|
|
pubs.organisational-group |
/University of Technology Sydney |
|
|
pubs.organisational-group |
/University of Technology Sydney/Faculty of Science |
|
|
pubs.organisational-group |
/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences |
|
|
utslib.copyright.status |
open_access |
* |
|
utslib.copyright.embargo |
2023-04-15T00:00:00+1000Z |
|
|
dc.date.updated |
2022-03-20T00:20:59Z |
|
|
pubs.publication-status |
Published online |
|
