Head of Department
Owheo Building, Room G.31
Ph:+64 3 479 8586
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.
Please look on my research pages for more details on my research interests, publications, links, etc.
Inaugural Professorial Lecture, 16th of April 2013, can be viewed here (237MB) or listened to here (67MB).
Publications
Albert, M., & Tannock, M. (2021). Prolific permutations. Electronic Journal of Combinatorics, 28(2), 2.2. doi: 10.37236/9966
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
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., & 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
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.
Edited Book - Research
Albert, M. H., & Nowakowski, R. J. (Eds.). (2009). Games of no chance 3. Cambridge University Press, 575p.
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 ACCV 2014: Lecture notes in computer science (Vol. 9003). (pp. 162-177). Cham, Switzerland: Springer. doi: 10.1007/978-3-319-16865-4_11
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., & Tannock, M. (2021). Prolific permutations. Electronic Journal of Combinatorics, 28(2), 2.2. doi: 10.37236/9966
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
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., & 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
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
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
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
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
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
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., 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., & Jelínek, V. (2016). Unsplittable classes of separable permutations. Electronic Journal of Combinatorics, 23(2), P2.49. Retrieved from http://www.combinatorics.org
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., Homberger, C., & Pantone, J. (2015). Equipopularity classes in the separable permutations. Electronic Journal of Combinatorics, 22(2), 2.2.
Albert, M., & Bouvel, M. (2015). A general theory of Wilf-equivalence for Catalan structures. Electronic Journal of Combinatorics, 22(4), P4.45.
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. 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
Albert, M. H., & Vatter, V. (2013). Generating and enumerating 321-avoiding and skew-merged simple permutations. Electronic Journal of Combinatorics, 20(2), P44.
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., 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. (2012). Young classes of permutations. Australasian Journal of Combinatorics, 54(2), 49-58.
Albert, M. H., & Nowakowski, R. J. (2012). Lattices of games. Order, 29(1), 75-84. doi: 10.1007/s11083-011-9198-0
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., 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., 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
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
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
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
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.
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., 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. (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., 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., 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., 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.
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., 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., & Atkinson, M. D. (2005). Simple permutations and pattern restricted permutations. Discrete Mathematics, 300, 1-15.
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., 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/
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.
Albert, M. H., & Nowakowski, R. J. (2004). Nim restrictions. Integers, 4. Retrieved from http://www.integers-ejcnt.org/vol4.html
