Papers

Preprint versions of most of my papers are also available on arXiv and the Murdoch Research Repository. Also see my Google Scholar Profile.

 

REFEREED JOURNAL PAPERS

• Counting Lyndon factors (with Jamie Simpson and W.F. Smyth), The Electronic Journal of Combinatorics 24(3) (2017) #P3.28 [preprint] [arXiv] [E-JC]
• Generalized trapezoidal words (with Florence Levé), Journal of Combinatorial Theory, Series A 136 (2015) 96-125. [preprint] [arXiv] [doi]
• The total run length of a word (with Jamie Simpson), Theoretical Computer Science 501 (2013) 41-48. [preprint] [arXiv] [doi]
• Extremal properties of (epi)Sturmian sequences & distribution modulo 1 (with Jean-Paul Allouche), L’Enseignement Mathématique 56 (2010), 365-401. [preprint] [arXiv]
• On shortest crucial words avoiding abelian powers (with Sergey Avgustinovich, Bjarni V. Halldórsson, Sergey Kitaev), Discrete Applied Mathematics 158 (2010), 605-607. [preprint] [arXiv] [doi]
• Crucial abelian k-power-free words (with Bjarni V. Halldórsson, Sergey Kitaev), Discrete Mathematics and Theoretical Computer Science, 12 (2010), 83-96.  [preprint] [arXiv] [journal]
• Distribution modulo 1 and the lexicographic world (with Jean-Paul Allouche), Annales des sciences mathématiques du Québec 33 (2009), 125-143. [preprint] [arXiv] [journal]
• Episturmian words: a survey (with Jacques Justin), RAIRO – Theoretical Informatics and Applications 43 (2009), 402-433. [preprint] [arXiv] [doi]
• A new characteristic property of rich words – extended version (with Michelangelo Bucci, Alessandro De Luca, Luca Q. Zamboni), Theoretical Computer Science 410 (2009), 2860-2863. [preprint] [arXiv] [doi]
• A connection between palindromic and factor complexity using return words (with Michelangelo Bucci, Alessandro De Luca, Luca Q. Zamboni), Advances In Applied Mathematics 42 (2009), 60-74. [preprint] [arXiv] [doi]
• Palindromic richness (with Jacques Justin, Steve Widmer, Luca Q. Zamboni), European Journal of Combinatorics 30 (2009), 510-531. [preprint] [arXiv] [doi]
• Directive words of episturmian words: equivalences and normalization (with Florence Levé, Gwénaël Richomme), RAIRO – Theoretical Informatics and Applications 43 (2009), 299-319. [preprint] [arXiv] [doi]
• Quasiperiodic and Lyndon episturmian words (with Florence Levé, Gwénaël Richomme), Theoretical Computer Science 409 (2008), 578-600. [preprint] [arXiv] [doi]
• Rich, Sturmian, and Trapezoidal words (with Aldo de Luca, Luca Q. Zamboni), Theoretical Computer Science 407 (2008), 569-573. [preprint] [arXiv] [doi]
• A note on the Markoff condition and central words (with Aaron Lauve, Franco V. Saliola), Information Processing Letters 105 (2008), 241-244. [preprint] [arXiv] [doi]
• Characterizations of finite and infinite episturmian words via lexicographic orderings (with Jacques Justin, Giuseppe Pirillo), European Journal of Combinatorics 29 (2008), 45-58. [preprint] [arXiv] [doi]
• A characterization of fine words over a finite alphabet, Theoretical Computer Science 391 (2008), 51-60. Files: [preprint] [arXiv] [doi]
• On the critical exponent of generalized Thue-Morse sequences (with Alexandre Blondin-Massé, Srecko Brlek, Sébastien Labbé), Discrete Mathematics & Theoretical Computer Science 9 (2007), 293-304. Files: [preprint] [arXiv] [journal]
• Powers in a class of A-strict standard episturmian words, Theoretical Computer Science 380 (2007), 330-354. [preprint] [arXiv] [doi]
• Occurrences of palindromes in characteristic Sturmian words, Theoretical Computer Science 352 (2006), 31-46. [preprint] [arXiv] [doi]
• Conjugates of characteristic Sturmian words generated by morphisms, European Journal of Combinatorics 25 (2004), 1025-1037. [preprint] [arXiv] [doi]
• Euler and his contribution to Number Theory (with Paul Scott), Australian Mathematics Teacher 60 (2004), 2-5. [preprint]

BOOK CHAPTERS

• Crucial words for abelian powers (with Bjarni V. Halldórsson, Sergey Kitaev), Lecture Notes in Computer Science, vol. 5583, Springer-Verlag, Berlin, 2009, pp. 264-275. [arXiv] [doi]

CONFERENCE PAPERS

• On the number of palindromically rich words, 59th Annual Meeting of the Australian Mathematical Society, Flinders University, Adelaide, South Australia, September 28 – October 1, 2015. [abstract] [proceedings] [slides]
• Palindromically rich GT-words, 38th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (38ACCMCC), Victoria University of Wellington, New Zealand, December 1-5, 2014.  [abstract] [proceedings] [slides]
• A note on self-maximal numbers, 37th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (37ACCMCC), The University of Western Australia, Perth, December 9-12, 2013.  [abstract] [proceedings]
• On a generalisation of trapezoidal words (with Florence Levé), 35th Australasian Conference on Combinatorial Mathematics & Combinatorial Computing (35ACCMCC), Monash University, Melbourne, Australia, December 5-9, 2011. [abstract] [proceedings]
• Crucial words for abelian powers (with Bjarni V. Halldórsson, Sergey Kitaev), in: V. Diekert et al. (Eds.), Proceedings of the 13th International Conference on Developments in Language Theory – DLT 2009 (Stuttgart, Germany), June 30 – July 3, 2009. [preprint] [arXiv]
• A new characteristic property of rich words (with Michelangelo Bucci, Alessandro De Luca, Luca Q. Zamboni), 12èmes Journées Montoises d’Informatique Théorique (Mons, Belgium), Aug 27-30, 2008. Files: [preprint] [arXiv] [slides]
• Directive words of episturmian words (with Florence Levé, Gwénaël Richomme), 12èmes Journées Montoises d’Informatique Théorique (Mons, Belgium), Aug 27-30, 2008. [preprint]
• Order and quasiperiodicity in episturmian words, 6th International Conference on Words (Marseille, France), Sept 17-21, 2007. [ext. abs.] [slides]
• A characterization of fine words over a finite alphabet, CANT conference (Liege, Belgium), May 8-19, 2006. Files: [preprint] [slides]
• Powers in a class of A-strict standard episturmian words, 5th International Conference on Words, Montreal (Quebec, Canada), Sept 13–17, 2005. Publications du LaCIM 36 (2005), 249-263. [preprint] [slides]

OTHER RESEARCH PAPERS

• On Sturmian and episturmian words, and related topics (PhD thesis excerpt), Bulletin of the Australian Mathematical Society 74 (2006), 155-160. [preprint]
• On Sturmian and episturmian words, and related topics, PhD thesis, The University of Adelaide, Australia, April 2006, 191 pages.
• Transcendence of certain k-ary continued fraction expansions [preprint]
• Book Review of “Automatic Sequences: Theory, Applications, Generalizations”, by J.-P. Allouche and J. Shallit (2003), The Gazette of the Australian Mathematical Society, September issue. [View it here]
• On the period length of pseudorandom number sequences, Honours thesis, The University of Adelaide, Australia, November 2002, 100 pages.