papers
submitted
57. M. Elder, A. Piggott, F. Stober, A. Thumm, A. Weiß
Finite groups with geodetic Cayley graphs
56. M. Elder, G. Gardam, A. Piggott, D. Spriano and K, Townsend
Graphs and groups with unique geodesics
published
55. M . Elder, A. Piggott and K. Townsend
On k-geodetic graphs and groups
International Journal of Algebra and Computation 33(6), p.1169 - 1182, 2023
54. M . Elder and A. Piggott
On groups presented by inverse-closed finite convergent length-reducing rewriting systems
Journal of Algebra 627 pp.106-131, 2023
53. A. Bishop, M. Elder,
A virtually 2-step nilpotent group with polynomial geodesic growth
Algebra and Discrete Mathematics 32:2, pp. 21-28, 2022
52. D. Berdinsky, M. Elder and J. Taback
On the geometry of Cayley automatic groups
International Journal of Algebra and Computation 32:3, pp.383-409, 2022
51. H. Dietrich, M. Elder, A. Piggott, Y. Qiao, A. Weiß
The isomorphism problem for plain groups is in Σ_3^P
39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022) 26:1-26:14 Leibniz International Proceedings in Informatics (LIPIcs) v.219, 2022
50. M . Elder and A. Piggott
Rewriting systems, plain groups, and geodetic graphs
Theoretical Computer Science 903 pp.134-144, 2022
49. D. Berdinsky, M. Elder and P. Kruengthomya
Cayley polynomial-time computable groups
Information and Computation 288, 2022, 15 pages
48. L. Ciobanu, M. Elder,
The complexity of solution sets to equations in hyperbolic groups
Israel Journal of Mathematics 245, 869–920 2021
47. D. Berdinsky, M. Elder and J. Taback
Being Cayley automatic is closed under taking wreath product with virtually cyclic groups
Bulletin of the Australian Mathematical Society 104(3), pp.464-47, 2021
46. M. Elder, Y. K. Goh,
k-pop stack sortable permutations and 2-avoidance
Electronic Journal of Combinatorics 28:1 Article Number P1.54, 2021
45. V. Diekert, M. Elder,
Solutions to twisted word equations and equations in virtually free groups
International Journal of Algebra and Computation 30 (4) (2020) pp.731–819
44. L. Ciobanu, M. Elder,
Solutions sets to systems of equations in hyperbolic groups are EDT0L in PSPACE
46th International Colloquium on Automata, Languages, and Programming (ICALP 2019) Vol 132 pp.110:1-110:15
43. A. Bishop, M. Elder,
Bounded automata groups are co-ET0L
Language and Automata Theory and Applications, Springer International Publishing, pp. 82-94, 2019
42. M. Elder, C. Rogers,
On a theorem of Avez
Journal of Group Theory 22(3) 2019 (published online 20 Jan 2019)
41. M. Elder, C. Rogers,
Sub-dominant cogrowth behaviour and the viability of determining amenability numerically
Experimental Mathematics 28(1) 2019 (published online 22 Aug 2017)
40. L. Ciobanu, M. Elder, M. Ferov,
Applications of L systems to group theory
International Journal of Algebra and Computation 28:2, 2018, 309-329
39. M. Elder, Y. K. Goh,
Permutations sorted by a finite and an infinite stack in series
LATA 2018, Lecture Notes in Computer Science Vol 10792, April 2018
38. M. Elder, G. Willis,
Totally disconnected groups from Baumslag-Solitar groups
Infinite group theory from the past to the future, World Scientific, 2018, 51-79
37. V. Diekert, M Elder,
Solutions of twisted word equations, EDT0L languages, and context-free groups
Automata, Languages, and Programming, 44nd International Colloquium, ICALP 2017, Warsaw, Poland, July 10-14, 2017, Proceedings, 2017
36. L. Ciobanu, V. Diekert, M. Elder,
Solution sets for equations over free groups are EDT0L languages
International Journal of Algebra and Computation 26:5, 2016, 843-886
35. T. Brough, L. Ciobanu, M. Elder, G. Zetzsche,
Permutations of context-free, ET0L and indexed languages
Discrete Mathematics and Theoretical Computer Science 17:3, 2016, 167–178
34. M. Elder, J. Taback,
Thompson’s group F is 1-counter graph automatic
Groups, Complexity, Cryptology 2016
33. B. Burton, M. Elder, A. Kalka, S. Tillmann,
2-manifold recognition is in logspace
Journal of Computational Geometry 7(1) 70–85, 2016
32. M. Elder, A. Rechnitzer, E. J. Janse van Rensburg,
Random sampling of trivial words in finitely presented groups
Experimental Mathematics 24(4) 391–409, 2015
31. L. Ciobanu, V. Diekert, M. Elder,
Solution sets for equations over free groups are EDT0L languages
Automata, Languages, and Programming, 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part II, 134–145, 2015
30. J. Burillo, M. Elder,
Metric properties of Baumslag-Solitar groups
International Journal of Algebra and Computation 25(5) 799–811, 2015
29. M. Elder, G. Lee, A. Rechnitzer,
Permutations generated by a depth 2 stack and an infinite stack in series are algebraic
Includes sequence A245233, P0015
Electronic Journal of Combinatorics 22 (2015) Issue 2 article P2.16
28. C. Banks, M. Elder, G. Willis,
Simple groups of automorphisms of trees determined by their action on finite subtrees
Journal of Group Theory 18 (2015), 235–261
27. N. Davis, M. Elder, L. Reeves,
Non-contracting groups generated by (3,2)-automata
Algebra and Discrete Mathematics 17 (2014) Number 1 pages 20–32
26. M. Elder, J. Taback,
C-graph automatic groups.
Journal of Algebra 413 (2014) Issue 1 pages 289–319
25. M. Elder, A. Rechnitzer, E. J. Janse van Rensburg, T. Wong,
The cogrowth series for BS(N,N) is D-finite
Includes sequences A002894 -- A229652
International Journal of Algebra and Computation 24 (2014) Issue 2 pages 171–187
24. M. Elder, G. Elston, G. Ostheimer,
On groups that have normal forms computable in logspace
Journal of Algebra 381 (2013) Issue 1 pages 260–281
23. M. Elder, A. Rechnitzer, T. Wong,
On the cogrowth of Thompson's group F
Groups, Complexity, Cryptology 4 (2012) Issue 2 pages 301–320
Includes sequence A246877
22. M. Bridson, J. Burillo, M. Elder, Z. Sunic,
On groups whose geodesic growth is polynomial
International Journal of Algebra and Computation 2 (2012) Number 5
21. M. Elder,
A linear time algorithm to compute geodesics in solvable Baumslag-Solitar groups
Illinois Journal of Mathematics 54 (2010) Number 1 pages 109–128
20. M. Elder, A. Rechnitzer,
Some geodesic problems in groups
Groups, Complexity, Cryptology 2 (2010) Issue 2 pages 223–229
19. M. Elder, E. Fusy, A. Rechnitzer,
Counting elements and geodesics in Thompson's group F
Journal of Algebra 324 (2010) Issue 1 pages 102-121
Includes sequences A156945 and A156946
18. S. Cleary, M. Elder, A. Rechnitzer, J. Taback,
Random subgroups of Thompson's group F
Groups, Geometry, Dynamics 4 (2010) Issue 1 pages 91-126
Includes sequence A111713
17. W. Dison, M. Elder, T. Riley, R. Young,
The Dehn function of Stallings' group.
Geometric and Functional Analysis 19 (2009) Number 2 pages 406-422
16. M. Elder, M. Kambites, G. Ostheimer,
On groups and counter automata
International Journal of Algebra and Computation 18 (2008) Number 8 pages 1345 - 1364
15. M. Elder,
G-automata, counter languages and the Chomsky hierarchy
Proceedings of Groups St Andrews 2005, London Math. Soc. Lecture Note Ser. 339 (2007)
14. M. Elder,
Permutations generated by a stack of depth 2 and an infinite stack in series
Electronic Journal of Combinatorics 13 (2006) Issue 1 article R68
Includes sequence A245233, P0015
13. S. Cleary, M. Elder, J. Taback,
Cone types and geodesic languages for lamplighter groups and Thompson's group F
Journal of Algebra 303 (2006) Issue 2 pages 476-500
12. M.H. Albert, M. Elder, A. Rechnitzer, P. Westcott, M. Zabrocki,
On the Stanley-Wilf limit of 4231-avoiding permutations and a conjecture of Arratia
Advances in Applied Mathematics 36(2) Special Issue on Pattern Avoiding Permutations (2006) pages 96-105
Includes sequence A061552
11. M. Elder,
Regular languages and the falsification by fellow traveler property
Algebraic and Geometric Topology Vol 5 (2005), paper no. 8, pages 129-134
10. M. Elder,
A context-free and a 1-counter geodesic language for a Baumslag-Solitar group
Theoretical Computer Science Vol 339, Issues 2-3 (2005) 344--371
9. M. Elder, S. Hermiller,
Minimal almost convexity
Journal of Group Theory Vol 8, No 2 (2005) 239--266
8. M. Elder, J. McCammond,
CAT(0) is an algorithmic property
Geometriae Dedicata Vol 107, No 1 (2004) 25--46
7. M. Elder,
Lδ groups are almost convex and have sub-cubic Dehn function
Algebraic and Geometric Topology Vol 4 (2004) 23--29
6. M. Elder,
A non-Hopfian almost convex group
Journal of Algebra Vol 271, No 1 (2004) 11--21
5. M. Elder,
The loop shortening property and almost convexity
Geometriae Dedicata Vol 102 No 1 (2003) 1--18
4. M. Elder, J. McCammond, J. Meier,
Combinatorial conditions that imply word-hyperbolicity for 3-manifolds
Topology Vol 42, Issue 6, (2003) 1241--1259
3. M. Elder,
Patterns theory and geodesic automatic structure
International Journal of Algebra and Computation Vol 13, No 2 (2003) 203--230
2. M. Elder, J. McCammond,
Curvature testing in 3-dimensional metric polyhedral complexes
Experimental Mathematics Vol 11, No 1 (2002) 143--158
1. M. Elder,
Finiteness and the falsification by fellow traveler property
Geometriae Dedicata Vol 95 (2002) 103--113.
software
1. M. Elder, J. McCammond,
survey articles
3. M. Elder,
Is F automatic?
Oberwolfach Reports, June 2018
2. M. Elder,
A short introduction to self-similar groups
AustMS Gazette Vol 39, No 3 (2012). Reprinted in Asia Pacific Mathematics Newsletter, Vol 3, No 1 (2013)
1. M. Elder, V. Vatter
Problems and Conjectures presented at the Third International Conference on Permutation Patterns, University of Florida, March 7-11, 2005
theses
2. M. Elder,
Automaticity, almost convexity and falsification by fellow traveler properties of some finitely presented groups
PhD Thesis, The University of Melbourne, 2000
(ranked as one of the most unusual thesis titles in Australia over a 20 year period by http://hdl.handle.net/10536/DRO/DU:30028653)
1. M. Elder,
Coxeter groups and the Moussong Complex
MSc Thesis, The University of Melbourne, 1996.
books edited
1. J. Burillo, S. Cleary, M. Elder, J. Taback and E. Ventura (eds) Geometric methods in group theory。Contemporary Mathematics 372, American Mathematical Society, Providence, RI, 2005
see also https://arxiv.org/a/elder_m_1.html
orcid.org/0000-0002-2438-3945
