My background is in mathematics, particularly in algebra, combinatorics, and logic. These areas all relate to the theoretical side of computer science, specifically the study of (effective) computability, and the representation and manipulation of data.
I am particularly interested in algorithms for counting (either exactly or approximately), sampling from, or manipulating combinatorial objects. I am an enthusiastic advocate of the use of computing resources in problem solving activities of all types. The study of combinatorial games is a particularly fruitful source of such problems, and also provides illustrations of the thesis that some hard computational problems can be rendered much simpler by a suitable change of perspective.
Inaugural Professorial Lecture, 16th of April 2013, can be viewed here (237MB) or listened to here (67MB).
Albert, M., Gudmundsson, B., & Ulfarsson, H. (2022). Collatz meets Fibonacci. Mathematics Magazine, 95(2), 130-136. doi: 10.1080/0025570X.2022.2023307
Journal - Research Article
Albert, M., Jelínek, V., & Opler, M. (2021). Two examples of Wilf-collapse. Discrete Mathematics & Theoretical Computer Science, 22(2), 9. doi: 10.46298/DMTCS.5986
Journal - Research Article
Albert, M., & Tannock, M. (2021). Prolific permutations. Electronic Journal of Combinatorics, 28(2), 2.2. doi: 10.37236/9966
Journal - Research Article
Albert, M., & Vatter, V. (2020). How many pop-stacks does it take to sort a permutation? arXiv. Retrieved from https://arxiv.org/abs/2012.05275
Working Paper; Discussion Paper; Technical Report
Albert, M., Holmgren, C., Johansson, T., & Skerman, F. (2020). Embedding small digraphs and permutations in binary trees and split trees. Algorithmica, 82(3), 589-615. doi: 10.1007/s00453-019-00667-5
Journal - Research Article
Albert, M., Bouvel, M., & Féray, V. (2020). Two first-order logics of permutations. Journal of Combinatorial Theory, Series A, 171, 105158. doi: 10.1016/j.jcta.2019.105158
Journal - Research Article
Albert, M., & Li, J. (2019). Wilf-collapse in permutation classes having two basis elements of size three. Australasian Journal of Combinatorics, 73(3), 440-455.
Journal - Research Article
Albert, M., & Vatter, V. (2019). An elementary proof of Bevan's Theorem on the growth of grid classes of permutations. Proceedings of the Edinburgh Mathematical Society, 62, 975-984. doi: 10.1017/S0013091519000026
Journal - Research Article
Albert, M., Brignall, R., Ruškuc, N., & Vatter, V. (2019). Rationality for subclasses of 321-avoiding permutations. European Journal of Combinatorics, 78, 44-72. doi: 10.1016/j.ejc.2019.01.001
Journal - Research Article
Albert, M., & Li, J. (2019). Uniquely-Wilf classes. Discrete Mathematics & Theoretical Computer Science, 21(2), 7. doi: 10.23638/DMTCS-21-2-7
Conference Contribution - Published proceedings: Full paper
Albert, M., & Tannock, M. (2019). Prolific compositions. Discrete Mathematics & Theoretical Computer Science, 21(2), 10. doi: 10.23638/DMTCS-21-2-7
Conference Contribution - Published proceedings: Full paper
Albert, M., & Tannock, M. (2019). Prolific compositions. arXiv. Retrieved from https://arxiv.org/abs/1904.05533
Working Paper; Discussion Paper; Technical Report
Alber, M. (2019, May). Wilf-equivalence and Wilf-collapse. Mathematics Seminar Series, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand. [Department Seminar].
Other Research Output
Albert, M. H., Homberger, C., Pantone, J., Shar, N., & Vatter, V. (2018). Generating permutations with restricted containers. Journal of Combinatorial Theory, Series A, 157, 205-232. doi: 10.1016/j.jcta.2018.02.006
Journal - Research Article
Ombler, F., Albert, M., & Hansen, P. (2018). How significant are "high" correlations between EQ-5D value sets? Medical Decision Making, 38(6), 635-645. doi: 10.1177/0272989x18778295
Journal - Research Article
Albert, M., Atminas, A., & Brignall, R. (2017). Characterising inflations of monotone grid classes of permutations. Journal of Combinatorial Theory, Series A, 154, 444-463. doi: 10.1016/j.jcta.2017.09.004
Journal - Research Article
Kennedy, E., Albert, M., & Nicholson, H. (2017). Do longus capitis and colli really stabilise the cervical spine? A study of their fascicular anatomy and peak force capabilities. Musculoskeletal Science & Practice, 32, 104-113. doi: 10.1016/j.msksp.2017.10.005
Journal - Research Article
Kennedy, E., Albert, M., & Nicholson, H. (2017). The fascicular anatomy and peak force capabilities of the sternocleidomastoid muscle. Surgical & Radiologic Anatomy, 39(6), 629-645. doi: 10.1007/s00276-016-1768-9
Journal - Research Article
Albert, M., Engen, M., Pantone, J., & Vatter, V. (2017). Universal layered permutations. arXiv. Retrieved from https://arxiv.org/abs/1710.04240
Working Paper; Discussion Paper; Technical Report
Ombler, F., Albert, M., & Hansen, P. (2017). The true significance of 'high' correlations between EQ-5D value sets [Economics Discussion Papers No. 1704]. Dunedin, New Zealand: School of Business, University of Otago. 20p. Retrieved from http://hdl.handle.net/10523/7247
Working Paper; Discussion Paper; Technical Report
Albert, M., & Brignall, R. (2016). 2 x 2 monotone grid classes are finitely based. Discrete Mathematics & Theoretical Computer Science, 18(2), 1. Retrieved from https://dmtcs.episciences.org/
Journal - Research Article
Albert, M., & Jelínek, V. (2016). Unsplittable classes of separable permutations. Electronic Journal of Combinatorics, 23(2), P2.49. Retrieved from http://www.combinatorics.org
Journal - Research Article
Albert, M., Lackner, M.-L., Lackner, M., & Vatter, V. (2016). The complexity of pattern matching for 321-avoiding skew-merged permutations. Discrete Mathematics & Theoretical Computer Science, 18(2), 11. Retrieved from https://dmtcs.episciences.org/
Journal - Research Article
Albert, M., & McKague, M. (2016). Quantum vs. classical parallelism. In A. B. Deb & N. Kjærgaard (Eds.), Proceedings of the Matariki Workshop on Quantum Science. (pp. 22). Retrieved from http://quantum.otago.ac.nz/mqs2016.html
Conference Contribution - Published proceedings: Abstract
Fu, X., McCane, B., Mills, S., Albert, M., & Szymanski, L. (2016). Auto-JacoBin: Auto-encoder Jacobian binary hashing. arXiv. 17p. Retrieved from https://arxiv.org/abs/1602.08127
Working Paper; Discussion Paper; Technical Report
Fu, X., McCane, B., Mills, S., & Albert, M. (2015). NOKMeans: Non-Orthogonal K-means hashing. In D. Cremers, I. Reid, H. Saito & M.-H. Yang (Eds.), Computer Vision: 12th Asian Conference on Computer Vision 2014, revised selected papers, part 1: Lecture notes in computer science (Vol. 9003). (pp. 162-177). Cham, Switzerland: Springer. doi: 10.1007/978-3-319-16865-4_11
Chapter in Book - Research
Albert, M. H., Ruškuc, N., & Vatter, V. (2015). Inflations of geometric grid classes of permutations. Israel Journal of Mathematics, 205(1), 73-108. doi: 10.1007/s11856-014-1098-8
Journal - Research Article
Albert, M., & Bousquet-Mélou, M. (2015). Permutations sortable by two stacks in parallel and quarter plane walks. European Journal of Combinatorics, 43, 131-164. doi: 10.1016/j.ejc.2014.08.024
Journal - Research Article
Albert, M., & Bouvel, M. (2015). A general theory of Wilf-equivalence for Catalan structures. Electronic Journal of Combinatorics, 22(4), P4.45.
Journal - Research Article
Albert, M., Homberger, C., & Pantone, J. (2015). Equipopularity classes in the separable permutations. Electronic Journal of Combinatorics, 22(2), 2.2.
Journal - Research Article
Fu, X., McCane, B., Mills, S., & Albert, M. (2015). How to select hashing bits? A direct measurement approach. Proceedings of the International Conference on Image and Vision Computing New Zealand (IVCNZ). 20. IEEE. doi: 10.1109/IVCNZ.2015.7761538
Conference Contribution - Published proceedings: Full paper
Trotman, A., Albert, M., & Burgess, B. (2015). Optimal packing in simple-family codecs. Proceedings of the International Conference on the Theory of Information Retrieval (ICTIR). (pp. 337-340). New York: ACM. doi: 10.1145/2808194.2809483
Conference Contribution - Published proceedings: Full paper
Albert, M. H., & Brignall, R. (2014). Enumerating indices of Schubert varieties defined by inclusions. Journal of Combinatorial Theory, Series A, 123(1), 154-168. doi: 10.1016/j.jcta.2013.12.003
Journal - Research Article
Li, Y., Zhang, H., Huang, Z., & Albert, M. (2014). Optimal link scheduling for delay-constrained periodic traffic over unreliable wireless links. Proceedings of the Conference on Computer Communications (INFOCOM). (pp. 1465-1473). IEEE. doi: 10.1109/infocom.2014.6848081
Conference Contribution - Published proceedings: Full paper
Albert, M., & Bousquet-Mélou, M. (2014). Permutations sortable by two stacks in parallel and quarter plane walks [Extended Abstract]. Discrete Mathematics & Theoretical Computer Science, (pp. 585-596). [Abstract]
Conference Contribution - Published proceedings: Abstract
Albert, M. H., & Vatter, V. (2013). Generating and enumerating 321-avoiding and skew-merged simple permutations. Electronic Journal of Combinatorics, 20(2), P44.
Journal - Research Article
Albert, M. H., Atkinson, M. D., Bouvel, M., Ruškuc, N., & Vatter, V. (2013). Geometric grid classes of permutations. Transactions of the American Mathematical Society, 365(11), 5859-5881. doi: 10.1090/S0002-9947-2013-05804-7
Journal - Research Article
Fu, X., McCane, B., Albert, M., & Mills, S. (2013). Action recognition based on principal geodesic analysis. Proceedings of the 28th International Conference of Image and Vision Computing New Zealand (IVCNZ). (pp. 259-264). IEEE. doi: 10.1109/IVCNZ.2013.6727026
Conference Contribution - Published proceedings: Full paper
Albert, M. (2013, April). How to shuffle badly. University of Otago, Dunedin, New Zealand. [Inaugural Professorial Lecture].
Other Research Output
Albert, M. (2012). Young classes of permutations. Australasian Journal of Combinatorics, 54(2), 49-58.
Journal - Research Article
Albert, M. H., & Nowakowski, R. J. (2012). Lattices of games. Order, 29(1), 75-84. doi: 10.1007/s11083-011-9198-0
Journal - Research Article
Albert, M. H., Atkinson, M. D., & Brignall, R. (2012). The enumeration of three pattern classes using monotone grid classes. Electronic Journal of Combinatorics, 19(3), P20.
Journal - Research Article
Zhang, H., Albert, M., & Willig, A. (2012). Combining TDMA with Slotted Aloha for delay constrained traffic over lossy links. Proceedings of the 12th International Conference on Control Automation Robotics & Vision (ICARCV). (pp. 701-706). IEEE. doi: 10.1109/ICARCV.2012.6485243
Conference Contribution - Published proceedings: Full paper
Albert, M. H., Atkinson, M. D., & Vatter, V. (2011). Subclasses of the separable permutations. Bulletin of the London Mathematical Society, 43(5), 859-870. doi: 10.1112/blms/bdr022
Journal - Research Article
Albert, M. H., Atkinson, M. D., Bouvel, M., Claesson, A., & Dukes, M. (2011). On the inverse image of pattern classes under bubble sort. Journal of Combinatorics, 2(2), 231-243.
Journal - Research Article
Albert, M. H., Linton, S., Ruškuc, N., Vatter, V., & Waton, S. (2011). On convex permutations. Discrete Mathematics, 311(8-9), 715-722. doi: 10.1016/j.disc.2011.01.009
Journal - Research Article
Albert, M., Cordón-Franco, A., van Ditmarsch, H., Fernández-Duque, D., Joosten, J. J., & Soler-Toscano, F. (2011). Secure communication of local states in interpreted systems. In A. Abraham, J. M. Corchado, S. Rodríguez González & J. F. De Paz Santana (Eds.), International Symposium on Distributed Computing and Artificial Intelligence: Advances in Intelligent and Soft Computing (Vol. 91). (pp. 117-124). Berlin, Germany: Springer. doi: 10.1007/978-3-642-19934-9
Conference Contribution - Published proceedings: Full paper
Albert, M. H., Atkinson, M. D., Brignall, R., Ruškuc, N., Smith, R., & West, J. (2010). Growth rates for subclasses of Av(321). Electronic Journal of Combinatorics, 17(1), R141.
Journal - Research Article
Albert, M., Atkinson, M., & Linton, S. (2010). Permutations generated by stacks and deques. Annals of Combinatorics, 14(1), 3-16. doi: 10.1007/s00026-010-0042-9
Journal - Research Article
Curry, B. W., Trotman, A., & Albert, M. (2010). Extricating meaning from Wikimedia article archives. Proceedings of the 15th Australasian Document Computing Symposium (ADCS). Retrieved from http://www.cs.rmit.edu.au/adcs2010/proceedings/
Conference Contribution - Published proceedings: Full paper
Albert, M. (2010). Young classes of permutations [Technical Report OUCS-2010-03]. Dunedin, New Zealand: Computer Science Department, University of Otago. 9p.
Working Paper; Discussion Paper; Technical Report
Albert, M. H., Aldred, R. E. L., Atkinson, M. D., Handley, C. C., Holton, D. A., McCaughan, D. J., & Sagan, B. E. (2009). Monotonic sequence games. In M. H. Albert & R. J. Nowakowski (Eds.), Games of no chance 3. (pp. 309-328). Cambridge University Press.
Chapter in Book - Research
Albert, M. H., & Linton, S. A. (2009). Growing at a perfect speed. Combinatorics, Probability & Computing, 18(3), 301-308. doi: 10.1017/s0963548309009699
Journal - Research Article
Albert, M. H., Atkinson, M. D., & Vatter, V. (2009). Counting 1324, 4231-avoiding permutations. Electronic Journal of Combinatorics, 16, R136.
Journal - Research Article
McCane, B., & Albert, M. (2008). Distance functions for categorical and mixed variables. Pattern Recognition Letters, 29(7), 986-993. doi: 10.1016/j.patrec.2008.01.021
Journal - Research Article
Albert, M. H. (2007). On the length of the longest subsequence avoiding an arbitrary pattern in a random permutation. Random Structures & Algorithms, 31(2), 227-238.
Journal - Research Article
Albert, M. H., Aldred, R. E. L., Atkinson, M. D., Van Ditmarsch, H. P., Handley, C. C., Holton, D. A., McCaughan, D. J., & Monteith, C. W. (2007). Cyclically closed pattern classes of permutations. Australasian Journal of Combinatorics, 38, 87-100.
Journal - Research Article
Albert, M. H., Aldred, R. E. L., Atkinson, M. D., Van Ditmarsch, H. P., Handley, C. C., Holton, D. A., & McCaughan, D. J. (2007). Compositions of pattern restricted sets of permutations. Australasian Journal of Combinatorics, 37, 43-56.
Journal - Research Article
Albert, M. H., Atkinson, M. D., & Brignall, R. (2007). Permutation classes of polynomial growth. Annals of Combinatorics, 11(3 - 4), 249-264. doi: 10.1007/s00026-007-0318-x
Journal - Research Article
Albert, M. H., Atkinson, M. D., Nussbaum, D., Sack, J. R., & Santoro, N. (2007). On the longest increasing subsequence of a circular list. Information Processing Letters, 101, 55-59. doi: 10.1016/j.ipl.2006.08.003
Journal - Research Article
Albert, M. H., Coleman, M., Flynn, R., & Leader, I. (2007). Permutations containing many patterns. Annals of Combinatorics, 11(3 - 4), 265-270. doi: 10.1007/s00026-007-0319-9
Journal - Research Article
Albert, M. H., Elder, M., Rechnitzer, A., Westcott, P., & Zabrocki, M. (2006). On the Stanley-Wilf limit of 4231-avoiding permutations and a conjecture of Arratia. Advances in Applied Mathematics, 36(2), 96-105.
Journal - Research Article
Albert, M. H., Atkinson, M. D., & Brignall, R. (2006). Permutation classes of polynominal growth [Technical Report OUCS-2006-05]. Dunedin, New Zealand: Computer Science Department, University of Otago. 17p.
Working Paper; Discussion Paper; Technical Report
Albert, M. H., Atkinson, M. D., Handley, C. C., Aldred, R. E. L., McCaughan, D. J., & Sagan, B. E. (2006). Monotonic sequence games [Technical Report OUCS-2006-04]. Dunedin, New Zealand: Computer Science Department, University of Otago. 20p.
Working Paper; Discussion Paper; Technical Report
Albert, M. H., Coleman, M., Flynn, R., & Leader, I. (2006). Permutations containing many patterns [Technical Report OUCS-2006-09]. Dunedin, New Zealand: Computer Science Department, University of Otago. 6p.
Working Paper; Discussion Paper; Technical Report
Albert, M. H., & Atkinson, M. D. (2005). Simple permutations and pattern restricted permutations. Discrete Mathematics, 300, 1-15.
Journal - Research Article
Albert, M. H., & Paterson, M. S. (2005). Bounds for the growth rate of meander numbers. Journal of Combinatorial Theory, Series A, 112, 250-262.
Journal - Research Article
Albert, M. H., Aldred, R. E. L., Atkinson, M. D., Handley, C. C., Holton, D. A., McCaughan, D. J., & van Ditmarsch, H. (2005). Sorting classes. Electronic Journal of Combinatorics, 12(1). Retrieved from http://www.combinatorics.org/
Journal - Research Article
Albert, M. H., Aldred, R. E. L., Atkinson, M. D., van Ditmarsch, H. P., & Handley, C. C. (2005). Safe communication for card players by combinatorial designs for two-step protocols. Australasian Journal of Combinatorics, 33, 33-46.
Journal - Research Article
Albert, M. H., Linton, S. J., & Ruškuc, N. (2005). The insertion encoding of permutations. Electronic Journal of Combinatorics, 12. Retrieved from http://www.combinatorics.org/Volume_12/PDF/v12i1r47.pdf
Journal - Research Article
Albert, M. H., Aldred, R. E. L., Atkinson, M. D., van Ditmarsch, H. P., Handley, C. C., & Holton, D. A. (2004). Restricted permutations and queue jumping [Note]. Discrete Mathematics, 287, 129-133.
Journal - Research Article
Albert, M. H., Golynski, A., Hamel, A. M., López-Ortiz, A., Rao, S. S., & Safari, M. A. (2004). Longest increasing subsequences in sliding windows [Note]. Theoretical Computer Science, 321, 405-414.
Journal - Research Article
Albert, M. H., & Atkinson, M. D. (2003). Sorting with a forklift. Electronic Journal of Combinatorics, 9(2), 1-23. Retrieved from http://www.combinatorics.org/Volume_9/PDF/v9i2r9.pdf
Journal - Research Article
Albert, M. H., Aldred, R. E., Atkinson, M. D., van Ditmarsch, H. P., Handley, B. D., & Handley, C. C. (2003). Longest subsequences in permutations. Australasian Journal of Combinatorics, 28, 225-238.
Journal - Research Article
Albert, M. H., Atkinson, M. D., & Ruskuc, N. (2003). Regular closed sets of permutations. Theoretical Computer Science, 306, 85-100.
Journal - Research Article
Albert, M. H., Le, H., & Small, C. G. (2003). Assessing landmark influence on shape variation. Biometrika, 90(3), 669-678.
Journal - Research Article
Albert, M. H., Atkinson, M. D., Handley, C. C., Holton, D., & Stromquist, W. (2002). On packing densities of permutations. Electronic Journal of Combinatorics, 9(1). Retrieved from http://www.combinatorics.org/
Journal - Research Article
Albert, M. H., & Atkinson, M. D. (2002). Sorting with a fork lift. In M. Penttonen & E. Meineche Schmidt (Eds.), Proceedings of Scandinavian Workshop on Algorithm Theory, Lecture Notes in Computer Science. 2368, (pp. 368-377). Berlin: Springer-Verlag. [Abstract]
Conference Contribution - Published proceedings: Abstract
Albert, M. H., & Nowakowski, R. J. (2001). The game of End-Nim. Electronic Journal of Combinatorics, 8(2), 12 pages. Retrieved from www.combinatronics.org/volume_8/v8i2toc.html
Journal - Research Article
Albert, M. H., Aldred, R. E., Atkinson, M. D., Handley, C. C., & Holton, D. (2001). Permutations of a multiset avoiding permutations of length 3. European Journal of Combinatorics, 22, 1021-1031.
Journal - Research Article
Albert, M. H., Aldred, R. E., Holton, D., & Sheehan, J. (2001). On 3*-connected graphs. Australasian Journal of Combinatorics, 24, 193-207.
Journal - Research Article
Albert, M. H., Holton, D., & Nowakowski, R. J. (2001). The ultimate categorical matching in a graph. Discrete Mathematics, 232, 1-10.
Journal - Research Article
Albert, M. H., Aldred, R. E., Atkinson, M. D., & Holton, D. (2001). Algorithms for pattern involvement in permutations. In P. Eades & T. Takaoka (Eds.), Algorithms and Computation: The Proceedings of the 12th International Symposium, ISAAC 2001. (pp. 355-366). Christchurch: Springer-Verlag. [Full Paper]
Conference Contribution - Published proceedings: Full paper
Albert, M. H., & Chowdhury, A. (1999). The rationals have an AZ-Enumeration. Journal of the London Mathematical Society, 59(2), 385-395.
Journal - Research Article