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Professor Michael Albert

Michael_226

Owheo Building, Room 2.52
Tel +64 3 479 8586
Email malbert@cs.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).

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Publications

Albert, M., Gudmundsson, B., & Ulfarsson, H. (2022). Collatz meets Fibonacci. Mathematics Magazine. Advance online publication. doi: 10.1080/0025570X.2022.2023307

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

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

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. H., Nowakowski, R. J., & Wolfe, D. (2007). Lessons in play: An introduction to combinatorial game theory. Wellesley, MA: A K Peters, 304p.

Authored Book - Research

Albert, M. H., & Nowakowski, R. J. (Eds.). (2009). Games of no chance 3. Cambridge University Press, 575p.

Edited 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

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.

Chapter in Book - Research

Albert, M., Gudmundsson, B., & Ulfarsson, H. (2022). Collatz meets Fibonacci. Mathematics Magazine. Advance online publication. doi: 10.1080/0025570X.2022.2023307

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., 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., 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., 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., & 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. 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., & 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. 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

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

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

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

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. 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

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. (2007). Compositions of pattern restricted sets of permutations. Australasian Journal of Combinatorics, 37, 43-56.

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., 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. (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

More publications...