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| Research Interests |
Well now that I'm a "professor", I think I should be allowed to admit that I'm interested in all areas of mathematics. My talent seems to be mainly for discrete and combinatorial things, so I'm particularly interested in anything that falls under Discrete Mathematics. This includes any possible applications in any other branch of science, though when it comes to modelling, I'm still more inclined to prove theorems than to run simulations (i.e.: am not a gifted programmer).
| Publications |
Current Preprints (see also
here) :
1. On the notion of balance in social network analysis (Updated: December 29).
PDF
2. (with Anders Martinsson) On the existence of accessible paths in various models of fitness landscapes (Updated: April 24). PDF
3. (with Dmitry Zhelezov) Can connected commuting graphs of finite groups have arbitrarily large diameter ? (August 30). PDF
4. Permutations all of whose patterns of a given length are distinct (June 6). PDF
Published Papers (see also
here) :
5. Limit points in the range of the commuting probability function on finite groups, J. Group Theory 16 (2013), no.2, 235-247. PDF
6. On m-covering families of Beatty sequences with irrational moduli, J. Number Theory 132 (2012), no.10, 2277-2296. PDF
7. Why should one expect to find long runs of (non)-Ramanujan primes ? (January 21). PDF
N.B.: This is purely a discussion paper, I do not intend to submit it to a journal. I was asked to make it available, in order to hopefully stimulate further investigation of Ramanujan primes.
8. A Cauchy-Davenport type result for arbitrary regular graphs,
Integers 11 (2011), 227-235.
PDF
9. (with Urban Larsson and Aviezri Fraenkel) Invariant and dual subtraction games resolving the Duchene-Rigo conjecture, Theoret. Comput. Sci. 412 (2011), 729-735. PDF
10. The postage stamp problem and essential subsets in integer bases, in: David and Gregory Chudnovsky (eds.), Additive Number Theory : Festschrift in Honor of the Sixtieth Birthday of Melvyn B. Nathanson , pp. 153-170. Springer-Verlag, New York (Sep. 1, 2010).
PDF
11. (with Peter Dukes and Sarada Herke) On the possible orders of a basis for a finite cyclic group. Electron. J. Combin. 17 (2010), no.1, Paper R79 (10pp). PDF
12. (with Desmond MacHale) Minimal odd order automorphism
groups. J. Group Theory 13 (2010), no.2, 243-256.
PDF.
13. Urban Larsson, Two-pile Nim with a restricted number of move-size imitations
(with an appendix by Peter Hegarty). Integers 9 (2009),
671-690. PDF.
14. Answers to two questions posed by Farhi concerning additive bases.
J. Number Theory 129 (2009), no.12, 3052-3058.
PDF
15. (with Steven J. Miller) When almost all sets are difference dominated.
Random Structures and Algorithms 35 (2009), no.1, 118-136.
PDF.
16. Essentialities in additive bases. Proc. Amer. Math. Soc. 137
(2009), no.5, 1657-1661.
PDF
17. Finite groups with an automorphism cubing a large fraction of
elements. Math. Proc. R. Ir. Acad. (Series A) 109 (2009), no.1,
79-99.
PDF.
18. The inverse problem for representation functions for general linear forms.
Integers 8 (2008), Paper A16, 17pp. (electronic)
PDF
19. Some explicit constructions of sets with more sums than differences.
Acta Arithmetica 130 (2007), no.1, 61-77. PDF.
20. Extremal subsets of {1,...,n} avoiding solutions to linear equations in
three variables. Electron. J. Combin. 14 (2007), Paper R74, 22pp.
(electronic) PDF
21. An improved upper bound on the maximum size of k-primitive sets. Integers 6 (2006), Paper A28, 5pp. (electronic) PDF
22. (with Urban Larsson) Permutations of the natural numbers with prescribed difference multisets. Integers 6 (2006), Paper A3, 25pp.
(electronic)
PDF
23. Soluble groups with an automorphism inverting many elements. Math. Proc. R. Ir. Acad. 105A (2005), no.1, 59-73. PDF
24. (with Andreas Baltz, Urban Larsson, Jonas Knape and Tomasz Schoen) The structure of maximum subsets of {1,...,n} with no solutions to a+b=kc. Electron. J. Combin. 12 (2005), Paper No. 19, 16pp. (electronic) PDF
25. A variant of the discrete isoperimetric problem. Ars Combin. 73 (2004), 263-274. PDF
26. Permutations avoiding arithmetic patterns. Electron. J. Combin. 11 (2004), no.1, Paper 39, 21pp. (electronic) PDF
27. On a conjecture of Zimmerman about group automorphisms. Arch. Math. (Basel) 80 (2003), no.1, 1-11. PDF
28. (with Desmond MacHale) Two-groups in which an automorphism inverts precisely half the elements. Bull. London Math. Soc. 30 (1998), no.2, 129-135. PDF
29. Autocommutator subgroups of finite groups. J. Algebra 190 (1997), no.2, 556-562.
30. Writing commutators of group commutators as products of cubes. Irish Math. Soc. Bull. 37 (1996), 25-29.
31. Automorphism groups of order p^2 q^2. Math. Proc. R. Ir. Acad. 95A (1995), no.2, 149-152.
32. Minimal abelian automorphism groups of finite groups. Rend. Sem. Mat. Univ. Padova 94 (1995), 121-135.
33. (with Desmond MacHale) Products of group commutators. Irish Math. Soc. Bull. 34 (1995), 14-21.
34. The absolute centre of a group. J. Algebra 169 (1994), no.3, 929-935.
35. Eisenstein Series for Orthogonal Groups. Ph.D. thesis, Princeton University, October 1998.
36. Finite Groups which Occur as Automorphism Groups, M.Sc. thesis, National University of Ireland, August 1994.
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Last modified: Fri Mar 01 19:10:00 CET 2013