Publications

 

Refereed Journal Articles

 

1        Class numbers and biquadratic reciprocity, Kenneth S. Williams and James D. Currie. Canadian Journal of Mathematics 34 (1982), No. 4, 969-988.

 

2        A Direct Proof of a Result of Thue, James D. Currie, Utilitas Mathematics, 25 (1984), 299-302.

 

3        Which graphs allow infinite non-repetitive walks?  Discrete Mathematics 87 (1991), 249-260.

 

4        A characterization of fractionally well-covered graphs, James Currie and Richard Nowakowski.  Ars Combinatoria 31 (1991), 93-96.

 

5        The number of order-preserving maps of fences and crowns, J.D. Currie and T.I. Visentin.  Order 8 (1991), 133-142.

 

6        Words without near-repetitions, J.D. Currie and A. Bendor-Samuel.  Canadian Mathematical Bulletin 35 (1992), 161-166.

 

7        Connectivity of distance graphs, J.D. Currie, Discrete Mathematics 103 (1992), 91-94.

 

8        Open problems in pattern avoidance, James D. Currie.  American Mathematical Monthly 100 (1993), 790-793.

 

9        A note on antichains of words, James D. Currie, Electronic Journal of Combinatorics (1995) 2, R21 (7pp).

 

10    On the structure and extendibility of k-power free words, James D. Currie, European Journal of Combinatorics 16 (1995), 111-124.

 

11    Cantor Sets and Dejean’s Conjecture, James D. Currie & Robert O. Shelton, Journal of Automata, Languages and Combinatorics 1 (1996) 2, 113-127.

 

12    Non-repetitive words: ages and essences, James D. Currie, Combinatorica 16 (1) (1996), 19-40.

 

13    Infinite Overlap-free Binary Words, J.P. Allouche, James D. Currie & J.O. Shallit, Electronic Journal of Combinatorics 5 (1) (1998) #R27.

 

14    Separating Words with Small Grammars, James D. Currie, Holger Peterson, John Michael Robson & Jeffrey Shallit, Journal of Automata, Languages & Combinatorics 4 (1999) 2, 101-110.

 

15    Words strongly avoiding fractional powers, Julien Cassaigne & James D. Currie, European J. Combin. 20 (1999) no. 8, 725 - 737.

 

16    Avoiding Patterns in the Abelian Sense, James D. Currie & Vaclav Linek, Canadian J. Math. 53(2001) no. 4, pp. 696 – 714

 

17    The metric dimension and metric independence of a graph, James D. Currie & Ortrud R. Oellermann, J. Combin. Math. Combin. Comput. 39 (2001), 157-167

 

18    No iterated morphism generates any Arson sequence of odd order, James D. Currie, Discrete Math. 259 (2002), no. 1-3, 277-283.

 

19    There are ternary circular square-free words of length n for n  ≥ 18, James D. Currie, Electron. J. Combin. 9 (2002), no. 1, Note 10, 7 pp. (electronic).

 

20    Counting endomorphisms of crown-like orders, James D. Currie & Terry I. Visentin, Order 19 (2002), no. 4, 305-317.

 

21    Non-repetitive tilings, James D. Currie & R. Jamie Simpson, Electron. J. Combin. 9 (2002), no. 1, Research Paper 28, 13 pp. (electronic).

 

22    What is the Abelian analogue of Dejean’s conjecture? James D. Currie, Grammars and automata for string processing, 237-242, Topics in Comput. Math. 9, Taylor & Francis, London, 2003.

 

23    Circular words avoiding patterns, James D. Currie & D. Sean Fitzpatrick, Developments in Language Theory, 6th International Conference, DLT 2002, Kyoto, Japan, September 18-21, 2002, Revised Papers. Lecture Notes in Computer Science 2450 Springer 2003, ISBN 3-540-40431-7

 

24    The fixing block method in combinatorics on words, James D. Currie & Cameron W. Pierce, Combinatorica, 23, Issue 4, pp. 571 - 584, (December 2003).

 

25    The set of k-power free words over Σ is empty or perfect. James D. Currie & Robert O. Shelton, European J. Combin. 24 (2003), no. 5, 573-580.

 

26    A word on 7 letters which is non-repetitive up to mod 5, James D. Currie & Erica Moodie, Acta Informatica 39 (2003), no. 6-7. pp. 451 – 468

 

27    The number of binary words avoiding Abelian fourth powers grows exponentially, James D. Currie, Theoret. Comput. Sci., Special Issue on Combinatorics of the Discrete Plane and Tilings, 319 , Issue 1-3 (June 2004), pp. 441-446

 

28    There exist binary circular 5/2+ power free words of every length, Ali Aberkane & James D. Currie, Electronic J. of Combin 11 (2004), R10.

 

29    The Number of Ternary Words Avoiding Abelian Cubes Grows Exponentially, Ali Aberkane, James D. Currie & Narad Rampersad, J. Int. Seq., Vol. 7 (2004), Article 04.2.7, 13 pp. (electronic)

 

30    Attainable lengths for circular binary words avoiding k powers, Ali Aberkane & James D. Currie, Bull. Belg. Math. Soc. Simon Stevin  12, no. 4 (2005), 525–534.

 

31    The Thue-Morse word contains circular 5/2+ power free words of every length, Ali Aberkane & James D. Currie, Theor. Comput. Sci. 332 (1-3): 573-581 (2005)

 

32    Pattern avoidance: themes and variations, James D. Currie, Theor. Comput. Sci. 339 (1): 7-18 (2005)

 

33    Binary words containing infinitely many overlaps, James D. Currie,  Narad, Rampersad & Jeffrey Shallit, Electron. J. Combin. 13 (2006), no. 1, Research Paper 82, 10 pp.

 

34    Dejean's conjecture and Sturmian words, Morteza Mohammad-Noori & James D. Currie, European J. Combin. 28 (3): 876-890 (2007).

 

35    The Brachistochrone and Related Curves: Implications for Teaching the History of Calculus, Jeff Babb & James Currie (2007), Sixth In- ternational Congress for the History of Science in Science Education: Constructing Scientic Understanding Through Contextual Teaching, P. Heering, P. & D. Osewold, D. (eds.) Frank & Timme, Berlin: 2007.

 

36    On Abelian 2-avoidable binary patterns, James D. Currie and Terry I. Visentin, Acta Informatica, 43 (8): 521-533 (2007).

 

37    Proof without words: Double Angle Formula via Area, James D. Currie, Math. Mag., Feb 2008, pp.62.

 

38    Palindrome positions in ternary square-free words, James D. Currie, Theoret. Comp. Sci. 396 (1-3): 254-257 (2008).

 

39    Long binary patterns are Abelian 2-avoidable, James D. Currie and Terry I. Visentin, Theoret. Comp. Sci. 409, pp. 432-437 (2008).

 

40    The Brachistochrone Problem: Mathematics for a Broad Audience via a Large Context Problem, Jeff Babb and James D. Currie, Mont. Math. Expos. vol.5 5, nos.2 & 3, p.169 (2008).

 

41    For each α > 2 there is an infinite binary word with critical exponent α , James D. Currie and Narad Rampersad, Elect. J. Combin. 15, N34 (2008).

 

42    Least periods of factors of infinite words, James D. Currie and Kalle Saari, RAIRO: ITA.Vol. 43, pp. 165-178(2009).

 

43    A cyclic binary morphism avoiding Abelian fourth powers, James D. Currie & Ali Aberkane, Theoret. Comp. Sci. 410(1): 44-52(2009).

 

44    There are k-uniform cubefree binary morphisms for all k ≥ 0, James D. Currie & Narad Rampersad, Discrete Applied Mathematics, Vol. 157, Issue 11, 2548-2551 (2009)

 

45    Dejean's conjecture holds for n ≥ 30, James D. Currie and Narad Rampersad ,Theoret. Comp. Sci. Vol. 410, 2885-2888 (2009).

 

46    Dejean's conjecture holds for n ≥ 27, James D. Currie and Narad Rampersad ,RAIRO, 43: 775-778 (2009).

 

47    Cubefree words with many squares, James D. Currie and Narad Rampersad, DMTCS 12:3, 29-34 (2010).

 

48    Infinite words containing squares at every position, James D. Currie and Narad Rampersad, RAIRO-Theor. Inf. Appl. 44, 113-124 (2010).

 

49    A proof of Dejean's conjecture, James D. Currie and Narad Rampersad, Mathematics of Computation, (2010).

 

50    Recurrent words with constant Abelian complexity, James D. Currie and Narad Rampersad, Advances in Applied Mathematics, (2010), doi:10.1016/j.aam.2010.05.001

 

51    Lexicographically least words in the orbit closure of the Rudin-Shapiro word, James D. Currie, Theoret. Comp. Sci., doi.org/10.1016/j.tcs.2011.04.036

 

Monograph

 

52. The Complexity of the Simplex Algorithm, James D. Currie. Carleton-Ottawa Lecture Note Series, 4, May 1985

 

Technical Reports

 

53. Search and Rescue On Canada's East Coast, J. Currie, C. Budd, (P. Aitchison, T. Berry, N. Corbett, L. Corbett, F. Di Moro,  S. Olafson, M. Pantel, M. Sianturi, D Slonowsky), Proceedings of the First Prairie Mathematics & Industry Workshop, Brandon University, Aug. 2000.

 

54. Extended Analysis of Sample Size Requirements for Random Audits to Detect Non-conformance by Farms in the Canadian On-Farm Food Safety (COFFS) Program, Jeff Babb and James D. Currie, February 2008.

 

55. Report to the Egg Farmers of Canada: Analysis of Sample Size Requirements for Random Audits to Detect Non-conformance by Farms in the Canadian On-Farm Food Safety (COFFS) Program, February 2009.

 

56. Security of PassRules: Preliminary Report (21 pp), June 5, 2010.

 

57. Security of PassRules: Final Report (36 pp), June 25, 2010

 

58. Security of PassRules , James D. Currie. Prepared for ItsMe Security, December 2010.

 

59. Sample Size Requirements for Random Audits to Detect Non-conformance by Farms in the Canadian On-Farm Food Safety (COFFS) Program, Jeff Babb and James D. Currie. Prepared for the COFFS Group, March 2011.