Email michael.albert@otago.ac.nz
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).
Publications
Albert, M. H., Bean, C., Claesson, A., Nadeau, É., Pantone, J., & Ulfarsson, H. (2026). Combinatorial exploration: An algorithmic framework for enumeration. Memoirs of the American Mathematical Society, 317(1611). doi: 10.1090/memo/1611 Journal - Research Article
Albert, M., Bouvel, M., Féray, V., & Noy, M. (2024). A logical limit law for 231-avoiding permutations. Discrete Mathematics & Theoretical Computer Science, 26(1). doi: 10.46298/dmtcs.11751 Journal - Research Article
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
2026
Journal - Research Article
Albert, M. H., Bean, C., Claesson, A., Nadeau, É., Pantone, J., & Ulfarsson, H. (2026). Combinatorial exploration: An algorithmic framework for enumeration. Memoirs of the American Mathematical Society, 317(1611). doi: 10.1090/memo/1611
2024
Journal - Research Article
Albert, M., Bouvel, M., Féray, V., & Noy, M. (2024). A logical limit law for 231-avoiding permutations. Discrete Mathematics & Theoretical Computer Science, 26(1). doi: 10.46298/dmtcs.11751
2022
Journal - Research Article
Albert, M., Gudmundsson, B., & Ulfarsson, H. (2022). Collatz meets Fibonacci. Mathematics Magazine, 95(2), 130-136. doi: 10.1080/0025570X.2022.2023307
2021
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
Albert, M., & Tannock, M. (2021). Prolific permutations. Electronic Journal of Combinatorics, 28(2), 2.2. doi: 10.37236/9966
2020
Journal - Research Article
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
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
Working Paper; Discussion Paper; Technical Report
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
2019
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.
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
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
Conference Contribution - Published proceedings: Full paper
Albert, M., & Li, J. (2019). Uniquely-Wilf classes. Discrete Mathematics & Theoretical Computer Science, 21(2), 7. doi: 10.23638/DMTCS-21-2-7
Albert, M., & Tannock, M. (2019). Prolific compositions. Discrete Mathematics & Theoretical Computer Science, 21(2), 10. doi: 10.23638/DMTCS-21-2-7
Working Paper; Discussion Paper; Technical Report
Albert, M., & Tannock, M. (2019). Prolific compositions. arXiv. Retrieved from https://arxiv.org/abs/1904.05533
Other Research Output
Alber, M. (2019, May). Wilf-equivalence and Wilf-collapse. Mathematics Seminar Series, Department of Mathematics & Statistics, University of Otago, Dunedin, New Zealand. [Department Seminar].
2018
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
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
2017
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
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
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
Working Paper; Discussion Paper; Technical Report
Albert, M., Engen, M., Pantone, J., & Vatter, V. (2017). Universal layered permutations. arXiv. Retrieved from https://arxiv.org/abs/1710.04240
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
2016
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/
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/
Albert, M., & Jelínek, V. (2016). Unsplittable classes of separable permutations. Electronic Journal of Combinatorics, 23(2), P2.49. Retrieved from http://www.combinatorics.org
Conference Contribution - Published proceedings: Abstract
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
Working Paper; Discussion Paper; Technical Report
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
2015
Chapter in Book - Research
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
Journal - Research Article
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
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
Albert, M., & Bouvel, M. (2015). A general theory of Wilf-equivalence for Catalan structures. Electronic Journal of Combinatorics, 22(4), P4.45.
Albert, M., Homberger, C., & Pantone, J. (2015). Equipopularity classes in the separable permutations. Electronic Journal of Combinatorics, 22(2), 2.2.
Conference Contribution - Published proceedings: Full paper
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
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
2014
Journal - Research Article
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
Conference Contribution - Published proceedings: Full paper
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: Abstract
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]
2013
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
Albert, M. H., & Vatter, V. (2013). Generating and enumerating 321-avoiding and skew-merged simple permutations. Electronic Journal of Combinatorics, 20(2), P44.
Conference Contribution - Published proceedings: Full paper
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
Other Research Output
Albert, M. (2013, April). How to shuffle badly. University of Otago, Dunedin, New Zealand. [Inaugural Professorial Lecture].
2012
Journal - Research Article
Albert, M. (2012). Young classes of permutations. Australasian Journal of Combinatorics, 54(2), 49-58.
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.
Albert, M. H., & Nowakowski, R. J. (2012). Lattices of games. Order, 29(1), 75-84. doi: 10.1007/s11083-011-9198-0
Conference Contribution - Published proceedings: Full paper
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
2011
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.
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
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
Conference Contribution - Published proceedings: Full paper
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
2010
Journal - Research Article
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.
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 Other
Atkinson, M., & Albert, M. (2010). Preface. Annals of Combinatorics, 14(1), 1. doi: 10.1007/s00026-010-0041-x
Conference Contribution - Published proceedings: Full paper
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/
Working Paper; Discussion Paper; Technical Report
Albert, M. (2010). Young classes of permutations [Technical Report OUCS-2010-03]. Dunedin, New Zealand: Computer Science Department, University of Otago. 9p.
2009
Edited Book - Research
Albert, M. H., & Nowakowski, R. J. (Eds.). (2009). Games of no chance 3. Cambridge University Press, 575p.
Chapter in Book - Research
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.
Journal - Research Article
Albert, M. H., Atkinson, M. D., & Vatter, V. (2009). Counting 1324, 4231-avoiding permutations. Electronic Journal of Combinatorics, 16, R136.
Albert, M. H., & Linton, S. A. (2009). Growing at a perfect speed. Combinatorics, Probability & Computing, 18(3), 301-308. doi: 10.1017/s0963548309009699
2008
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
2007
Authored Book - Research
Albert, M. H., Nowakowski, R. J., & Wolfe, D. (2007). Lessons in play: An introduction to combinatorial game theory. Wellesley, MA: A K Peters, 304p.
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.
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
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
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
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.
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.
2006
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.
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.
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.
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.
2005
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.
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
Albert, M. H., & Atkinson, M. D. (2005). Simple permutations and pattern restricted permutations. Discrete Mathematics, 300, 1-15.
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.
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/
2004
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.
Albert, M. H., & Nowakowski, R. J. (2004). Nim restrictions. Integers, 4. Retrieved from http://www.integers-ejcnt.org/vol4.html
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.
2003
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.
Albert, M. H., Atkinson, M. D., & Ruskuc, N. (2003). Regular closed sets of permutations. Theoretical Computer Science, 306, 85-100.
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
Albert, M. H., Atkinson, M. D., & Klazar, M. (2003). The enumeration of simple permutations. Journal of Integer Sequences, 6(4), 1-18. Retrieved from http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Albert/albert.pdf
Albert, M. H., Le, H., & Small, C. G. (2003). Assessing landmark influence on shape variation. Biometrika, 90(3), 669-678.
2002
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/
Conference Contribution - Published proceedings: Abstract
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]
2001
Journal - Research Article
Albert, M. H., Holton, D., & Nowakowski, R. J. (2001). The ultimate categorical matching in a graph. Discrete Mathematics, 232, 1-10.
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.
Albert, M. H., Aldred, R. E., Holton, D., & Sheehan, J. (2001). On 3*-connected graphs. Australasian Journal of Combinatorics, 24, 193-207.
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
Conference Contribution - Published proceedings: Full paper
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]
1999
Journal - Research Article
Albert, M. H., & Chowdhury, A. (1999). The rationals have an AZ-Enumeration. Journal of the London Mathematical Society, 59(2), 385-395.