研究领域

Combinatorics on words

My research interests fall under the broad areas of Combinatorics, Discrete Mathematics, and Number Theory. I am especially interested in combinatorics on words, from algebraic and geometric points of view, and its applications in Number Theory. Much of my research to date has focussed on repetitions (including abelian repetitions) and periodicity (including quasiperiodicity) in finite and infinite words (particularly Sturmian and episturmian words, including the well-known Fibonacci word, and also the Thue-Morse sequence), as well as other combinatorial regularities and patterns occurring in words, such as recurring factors, Lyndon words, palindromes, and related notions of word complexity, lexicographic ordering, and distribution of real numbers modulo 1 from a combinatorial perspective. Some of these topics have applications to a wide variety of other scientific fields, ranging from theoretical computer science (digital imagery, pattern recognition) to theoretical physics (quasicrystal modelling) and molecular biology (DNA sequences). I am happy to supervise Honours and PhD projects in any of the areas mentioned above. Feel free to e-mail me, or if you’re in Perth, drop by my office to discuss possible topics. To get an idea of the sorts of things I work on, see my publications or talks.

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Glen, A., Levé, F., (2015), Generalized trapezoidal words, Journal of Combinatorial Theory, Series A, 136, November 2015, pages 96 - 125. Glen, A., Simpson, J., (2013), The total run length of a word, Theoretical Computer Science, 501, , pages 41 - 48. Allouche, J., Glen, A., (2010), Extremal properties of (epi)Sturmian sequences and distribution modulo 1, L'Enseignement Mathematique. Monographies, 56, 2, pages 365 - 401. Glen, A., Halldórsson, B., Kitaev, S., (2010), Crucial abelian k-power-free words, Discrete Mathematics and Theoretical Computer Science (Online Edition), 12, 5, pages 83 - 96. Glen, A., Avgustinovich, S., Halldórsson, B., Kitaev, S., (2010), On shortest crucial words avoiding abelian powers, Discrete Applied Mathematics, 158, 6, pages 605 - 607. Glen, A., Allouche, J., (2009), Distribution modulo 1 and the lexicographic world, Annales des Sciences Mathematiques du Quebec, 33, 2, pages 125 - 143. Glen, A., Bucci, M., De Luca, A., Zamboni, L., (2009), A connection between palindromic and factor complexity using return words, Advances in Applied Mathematics, 42, 1, pages 60 - 74. Glen, A., Bucci, M., De Luca, A., Zamboni, L., (2009), A new characteristic property of rich words, Theoretical Computer Science, 410, , pages 2860 - 2863. Glen, A., Levé, F., Richomme, G., (2008), Quasiperiodic and Lyndon episturmian words, Theoretical Computer Science, 409, , pages 578 - 600. Glen, A., (2008), A characterization of fine words over a finite alphabet, Theoretical Computer Science, 391, , pages 51 - 60. Glen, A., Justin, J., Pirillo, G., (2008), Characterizations of finite and infinite episturmian words via lexicographic orderings, European Journal of Combinatorics, 29, 1, pages 45 - 58. Glen, A., Lauve, A., Saliola, F., (2008), A note on the Markoff condition and central words, Information Processing Letters, 105, , pages 241 - 244. Glen, A., (2007), Powers in a class of A-strict standard episturmian words, Theoretical Computer Science, 380, , pages 330 - 354. Glen, A., Blondin-Massé, A., Brlek, S., Labbé, S., (2007), On the Critical Exponent of Generalized Thue-Morse Words, Discrete Mathematics and Theoretical Computer Science (Online Edition), 9, 1, pages 293 - 304. Glen, A., (2006), Occurrences of palindromes in characteristic Sturmian words, Theoretical Computer Science, 352, , pages 31 - 46. Glen, A., (2006), On Sturmian and episturmian words, and related topics, Australian Mathematical Society. Bulletin, 74, , pages 155 - 160. Glen, A., (2004), Conjugates of characteristic Sturmian words generated by morphisms, European Journal of Combinatorics, 25, , pages 1025 - 1037. Glen, A., Scott, P., (2004), Euler and his contribution to Number Theory, Australian Mathematics Teacher, 60, 1, pages 2 - 5.