https://nova.newcastle.edu.au/vital/access/manager/Index en-au 5 Combinatorial conditions that imply word-hyperbolicity for 3-manifolds https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10972 Wed 18 Sep 2024 13:58:22 AEST ]]> The loop shortening property and almost convexity https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10971 Wed 18 Sep 2024 13:51:13 AEST ]]> A non-Hopfian almost convex group https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10970 Wed 18 Sep 2024 13:51:11 AEST ]]> Minimal almost convexity https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10969 Wed 18 Sep 2024 13:44:16 AEST ]]> CAT(0) is an algorithmic property https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10968 Wed 18 Sep 2024 13:44:14 AEST ]]> Lδ groups are almost convex and have sub-cubic Dehn function https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10967 Wed 18 Sep 2024 13:44:12 AEST ]]> On groups and counter automata https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9978 Wed 11 Apr 2018 17:01:17 AEST ]]> The Dehn function of Stallings' group https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9979 Wed 11 Apr 2018 16:16:17 AEST ]]> Finiteness and the falsification by fellow traveler property https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10975 Wed 11 Apr 2018 16:14:40 AEST ]]> Some geodesic problems in groups https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10979 Wed 11 Apr 2018 15:31:48 AEST ]]> On groups that have normal forms computable in logspace https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:12653 Wed 11 Apr 2018 15:25:06 AEST ]]> Cone types and geodesic languages for lamplighter groups and Thompson's group F https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9976 Wed 11 Apr 2018 15:20:32 AEST ]]> A linear time algorithm to compute geodesics in solvable Baumslag-Solitar groups https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10980 Wed 11 Apr 2018 15:10:44 AEST ]]> Curvature testing in 3-dimensional metric polyhedral complexes https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10974 Wed 11 Apr 2018 15:07:38 AEST ]]> Random subgroups of Thompson’s group F https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10978 Wed 11 Apr 2018 14:35:41 AEST ]]> A short introduction to self-similar groups https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:11509 Wed 11 Apr 2018 14:28:10 AEST ]]> The cogrowth series for BS (N;N) is D-Finite https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:14052 Nb = baN〉, which we show to be D-finite. It follows that their cogrowth rates are algebraic numbers.]]> Wed 11 Apr 2018 14:21:37 AEST ]]> Patterns theory and geodesic automatic structure https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10973 Wed 11 Apr 2018 13:55:17 AEST ]]> Regular languages and the falsification by fellow traveler property https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9973 Wed 11 Apr 2018 13:38:31 AEST ]]> G-automata, counter languages and the Chomsky hierarchy https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:11038 Wed 11 Apr 2018 12:43:12 AEST ]]> Solution sets for equations over free groups are EDT0L languages https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:21496 i≤sFi, where each Fi is either a free or finite group, or a free monoid with involution. In all cases the result is the same: the set of all solutions in reduced words is EDT0L. This was known only for quadratic word equations by, which is a very restricted case. Our general result became possible due to the recent recompression technique of Jeż. In this paper we use a new method to integrate solutions of linear Diophantine equations into the process and obtain more general results than in the related paper. For example, we improve the complexity from quadratic nondeterministic space in to quasi-linear nondeterministic space here. This implies an improved complexity for deciding the existential theory of non-abelian free groups: NSPACE(n log n). The conjectured complexity is NP, however, we believe that our results are optimal with respect to space complexity, independent of the conjectured NP.]]> Wed 11 Apr 2018 12:43:02 AEST ]]> On groups whose geodesic growth is polynomial https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:11143 Wed 11 Apr 2018 12:41:07 AEST ]]> Permutations generated by a stack of depth 2 and an infinite stack in series https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10977 Wed 11 Apr 2018 11:44:37 AEST ]]> Non-contracting groups generated by (3,2)-automata https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:14794 Wed 11 Apr 2018 11:20:20 AEST ]]> Solution sets for equations over free groups are EDT0L languages https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:24664 Wed 11 Apr 2018 10:32:23 AEST ]]> A context-free and a 1-counter geodesic language for a Baumslag-Solitar group https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9971 Wed 11 Apr 2018 10:19:49 AEST ]]> Counting elements and geodesics in Thompson's group F https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9982 Wed 11 Apr 2018 09:29:32 AEST ]]> C-graph automatic groups https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:14202 Tue 24 Aug 2021 14:39:23 AEST ]]> Permutations of context-free, ET0L and indexed languages https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:24663 Tue 10 Mar 2020 11:56:31 AEDT ]]> 2-manifold recognition is in logspace https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:24552 Tue 10 Mar 2020 11:56:08 AEDT ]]> Metric properties of Baumslag–Solitar groups https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:21495 Sat 24 Mar 2018 08:03:39 AEDT ]]> Random sampling of trivial words in finitely presented groups https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:18607 Sat 24 Mar 2018 08:01:04 AEDT ]]> Random sampling of trivial words in finitely presented groups https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:25144 Sat 24 Mar 2018 07:17:10 AEDT ]]> Thompson's group F is 1-counter graph automatic https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:24783 F is automatic. With the recent extensions of the notion of an automatic group to graph automatic by Kharlampovich, Khoussainov and Miasnikov and then to -graph automatic by the authors, a compelling question is whether F is graph automatic or C-graph automatic for an appropriate language class C. The extended definitions allow the use of a symbol alphabet for the normal form language, replacing the dependence on generating set. In this paper we construct a 1-counter graph automatic structure for F based on the standard infinite normal form for group elements.]]> Sat 24 Mar 2018 07:14:06 AEDT ]]> Simple groups of automorphisms of trees determined by their actions on finite subtrees https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:16694 Mon 19 Aug 2024 11:14:04 AEST ]]> Applications of L systems to group theory https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:48744 Mon 17 Apr 2023 13:56:08 AEST ]]> Problems and conjectures presented at the Third International Conference on Permutation Patterns (University of Florida, March 7-11, 2005) https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:11537 Mon 02 Sep 2024 12:01:33 AEST ]]> Permutations generated by a depth 2 stack and an infinite stack in series are algebraic https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:16984 Fri 30 Aug 2024 15:50:23 AEST ]]> On the Stanley–Wilf limit of 4231-avoiding permutations and a conjecture of Arratia https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:10341 Fri 13 Sep 2024 12:33:55 AEST ]]> Totally disconnected groups from Baumslag-Solitar groups https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:41852 Fri 12 Aug 2022 16:22:24 AEST ]]> On the cogrowth of Thompson's group F https://nova.newcastle.edu.au/vital/access/manager/Repository/uon:12424 Fri 05 Jul 2024 08:09:47 AEST ]]>