41. L. Ciobanu, M. Elder, M. Ferov,
Applications of L systems to group theory

40. M. Elder, C. Rogers,
Sub-dominant cogrowth behaviour and the viability of determining amenability numerically 

39. M. Elder, C. Rogers,
Algebraic structure of groups reflected in random walk distributions
arxiv: 1605.04065

to appear

40. 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


37. M. Elder, G. Willis,
Totally disconnected groups from Baumslag-Solitar groups

36. L. Ciobanu, V. Diekert, M. Elder,
Solution sets for equations over free groups are EDT0L languages

35. T. Brough, L. Ciobanu, M. Elder, G. Zetzsche,
Permutations of context-free, ET0L and indexed languages

34. M. Elder, J. Taback,
Thompson’s group is 1-counter graph automatic

33. B. Burton, M. Elder, A. Kalka, S. Tillmann,
2-manifold recognition is in logspace

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 -- conference version
30. J. Burillo, M. Elder, 
Metric properties of Baumslag-Solitar groups

29. M. Elder, G. Lee, A. Rechnitzer,
Permutations generated by a depth 2 stack and an infinite stack in series are algebraic
Includes sequence A245233P0015
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), 235261

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 171187

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 for finitely generated 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 A245233P0015

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,
δ 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.


1. M. Elder, J. McCammond, 

survey articles 

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


2. M. Elder,
Automaticity, almost convexity and falsification by fellow traveler properties of some finitely presented groups
PhD Thesis, The University of Melbourne, 2000
PDF (1752k)    
(ranked as one of the most unusual thesis titles in Australia over a 20 year period by

1. M. Elder,
Coxeter groups and the Moussong Complex
MSc Thesis, The University of Melbourne, 1996. 
PDF (345k)

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