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

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

33. T. Brough, L. Ciobanu, M. Elder,
Permutations of context-free and indexed languages

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

31. M. Elder, G. Lee, A. Rechnitzer,
Permutations generated by a stack of depth 2 and an infinite stack in series are algebraic
Includes sequence A245233

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

to appear 

29. M. Elder, A. Rechnitzer, E. J. Janse van Rensburg, 
Random sampling of trivial words in finitely presented groups. 


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
arxiv; nova

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
arxiv; nova

26. M. Elder, J. Taback,
C-graph automatic groups.
Journal of Algebra 413 (2014) Issue 1 pages 289–319
arxiv; nova

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
arxiv; nova

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
arxiv; nova

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
arxiv; nova

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
arxiv; nova

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
arxiv; nova

20. M. Elder, A. Rechnitzer,
Some geodesic problems for finitely generated groups.
Groups, Complexity, Cryptology 2 (2010) Issue 2 pages 223–229
arxiv; nova

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
arxiv; nova

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
arxiv; nova

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.
arxiv; nova

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.
arxiv; nova

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).
arxiv; nova

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 permutations P0015.
arxiv; nova

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
arxiv; nova

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.
arxiv; nova

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.
arxiv; nova

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
arxiv; nova

9. M. Elder, S. Hermiller,
Minimal almost convexity.
Journal of Group Theory Vol 8, No 2 (2005) 239--266 
arxiv; nova

8. M. Elder, J. McCammond,
CAT(0) is an algorithmic property.
Geometriae Dedicata Vol 107, No 1 (2004) 25--46
arxiv; nova

7. M. Elder,
Lδ groups are almost convex and have sub-cubic Dehn function.
Algebraic and Geometric Topology Vol 4 (2004) 23--29
arxiv; nova

6. M. Elder,
A non-Hopfian almost convex group.
Journal of Algebra Vol 271, No 1 (2004) 11--21
arxiv; nova

5. M. Elder,
The loop shortening property and almost convexity.
Geometriae Dedicata Vol 102 No 1 (2003) 1--18
arxiv; nova

4. M. Elder, J. McCammond, J. Meier,
Combinatorial conditions that imply word-hyperbolicity for 3-manifolds.
Topology Vol 42, Issue 6, (2003) 1241--1259
arxiv; nova

3. M. Elder,
Patterns theory and geodesic automatic structure.
International Journal of Algebra and Computation Vol 13, No 2 (2003) 203--230
arxiv; nova

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.
arxiv; nova


1. M. Elder, J. McCammond, 
homepagehow to usegap code

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)
nova; Solutions

1. M. Elder, V. Vatter
Problems and Conjectures presented at the Third International Conference on Permutation Patterns, University of Florida, March 7-11, 2005.
arxiv; nova


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.

(nova is the university of newcastle's digital repository for journal articles, click on this link for the published version or author final version as permitted by the publisher)