My Research




Research Interests

Publications

Research Students

Some Random Conference Presentations



Research Interests

The numbers refer to items in my list of publications below

Combinatorial Number Theory: 4, 13, 14, 15, 17, 18, 21, 22, 23, 25, 26, 27, 28, 29

Combinatorial Games: 16, 20, 29

Other Combinatorics: 10, 15, 32

Finite Group Theory: 5, 9, 11, 19, 24, 30, 34, 35, 36, 37, 38, 39, 40, 43

Discrete Probability: 3, 5, 7, 8, 9, 14, 22

Analytic Number Theory: 42

Applications (Opinion Dynamics, Distributed Computing, Social Networks, Modelling of Evolution): 1, 2, 3, 7, 8, 9, 12

The items which intersect more than one category are: 3, 5, 7, 8, 9, 14, 22, 29


Publications

Current Preprints (see also here) :

Published Papers (see also here) :

1. (with Anders Martinsson and Edvin Wedin) The Hegselmann-Krause dynamics on the circle converge, J. Difference Equ. Appl. 22 (2016), no. 11, 1720--1731. PDF

2. (with Edvin Wedin) The Hegselmann-Krause dynamics for equally spaced agents, J. Difference Equ. Appl. 22 (2016), no. 11, 1621--1645. PDF

3. (with Anders Martinsson and Dmitry Zhelezov) When can multi-agent rendezvous be executed in time linear in the diameter of a plane configuration? Proceedings of 17th International Conference on Distributed Computing and Networking (ICDCN '16). PDF.

Note: The above item is a reworked version of this earlier preprint.

4. (with Anders Martinsson) Permutations destroying arithmetic progressions in finite cyclic groups, Electron. J. Combin. 22 (2015), no. 4, Paper #P4.39, 14pp. PDF

5. (with Dmitry Zhelezov) Can connected commuting graphs of finite groups have arbitrarily large diameter ? In: Geometry, structure and randomness in combinatorics, CRM Series, No. 18, Ed. Norm., Pisa (2015), pp. 141--144. PDF

Note: This paper is really just an extended abstract of item nr. 10 below, but was published as part of a conference proceedings.

6. (with Edvin Wedin) The Hegselmann-Krause dynamics for the continuous-agent model and a regular opinion function do not always lead to consensus, IEEE Trans. Automat. Control 60 (2015), no. 9, 2416--2421. PDF

7. (with Edvin Wedin) A quadratic lower bound for the convergence rate in the one-dimensional Hegselmann-Krause bounded confidence dynamics, Discrete Comput. Geom. 53 (2015), no. 2, 478--486. PDF

8. (with Anders Martinsson) On the existence of accessible paths in various models of fitness landscapes, Ann. Appl. Probab. 24 (2014), no. 4, 1375--1395. PDF

9. (with Dmitry Zhelezov) On the diameters of commuting graphs arising from random skew-symmetric matrices, Combin. Probab. Comput. 23 (2014), no. 3, 449--459. PDF

10. Permutations all of whose patterns of a given length are distinct, J. Combin. Theory (Series A) 120 (2013), no. 7, 1663--1671. PDF

11. Limit points in the range of the commuting probability function on finite groups, J. Group Theory 16 (2013), no.2, 235--247. PDF

12. On the notion of balance in social network analysis. Internal report. PDF

13. On m-covering families of Beatty sequences with irrational moduli, J. Number Theory 132 (2012), no. 10, 2277--2296. PDF

14. Why should one expect to find long runs of (non)-Ramanujan primes? (January 21, 2012). PDF

Note: 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.

15. A Cauchy-Davenport type result for arbitrary regular graphs, Integers 11 (2011), 227--235. PDF

16. (with Urban Larsson and Aviezri Fraenkel) Invariant and dual subtraction games resolving the Duchene-Rigo conjecture, Theoret. Comput. Sci. 412 (2011), 729--735. PDF

17. 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

18. (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

19. (with Desmond MacHale) Minimal odd order automorphism groups. J. Group Theory 13 (2010), no. 2, 243--256. PDF.

20. 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.

21. Answers to two questions posed by Farhi concerning additive bases. J. Number Theory 129 (2009), no. 12, 3052--3058. PDF

22. (with Steven J. Miller) When almost all sets are difference dominated. Random Structures and Algorithms 35 (2009), no. 1, 118--136. PDF.

23. Essentialities in additive bases. Proc. Amer. Math. Soc. 137 (2009), no. 5, 1657--1661. PDF

24. 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.

25. The inverse problem for representation functions for general linear forms. Integers 8 (2008), Paper A16, 17pp. (electronic) PDF

26. Some explicit constructions of sets with more sums than differences. Acta Arithmetica 130 (2007), no. 1, 61--77. PDF.

27. Extremal subsets of {1,...,n} avoiding solutions to linear equations in three variables. Electron. J. Combin. 14 (2007), Paper R74, 22pp. (electronic) PDF

28. An improved upper bound on the maximum size of k-primitive sets. Integers 6 (2006), Paper A28, 5pp. (electronic) PDF

29. (with Urban Larsson) Permutations of the natural numbers with prescribed difference multisets. Integers 6 (2006), Paper A3, 25pp. (electronic) PDF

30. Soluble groups with an automorphism inverting many elements. Math. Proc. R. Ir. Acad. 105A (2005), no. 1, 59--73. PDF

31. (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

32. A variant of the discrete isoperimetric problem. Ars Combin. 73 (2004), 263--274. PDF

33. Permutations avoiding arithmetic patterns. Electron. J. Combin. 11 (2004), no. 1, Paper 39, 21pp. (electronic) PDF

34. On a conjecture of Zimmerman about group automorphisms. Arch. Math. (Basel) 80 (2003), no. 1, 1--11. PDF

35. (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

36. Autocommutator subgroups of finite groups. J. Algebra 190 (1997), no. 2, 556--562.

37. Writing commutators of group commutators as products of cubes. Irish Math. Soc. Bull. 37 (1996), 25--29.

38. Automorphism groups of order p^2 q^2. Math. Proc. R. Ir. Acad. 95A (1995), no. 2, 149--152.

39. Minimal abelian automorphism groups of finite groups. Rend. Sem. Mat. Univ. Padova 94 (1995), 121--135.

40. (with Desmond MacHale) Products of group commutators. Irish Math. Soc. Bull. 34 (1995), 14--21.

41. The absolute centre of a group. J. Algebra 169 (1994), no. 3, 929--935.

Theses :

42. Eisenstein Series for Orthogonal Groups. Ph.D. thesis, Princeton University, October 1998.

43. Finite Groups which Occur as Automorphism Groups, M.Sc. thesis, National University of Ireland, August 1994.


Research Students

PhD students :

Edvin Wedin (2015-):

Anders Martinsson (2012-): Licentiate thesis, Ph.D. thesis

Dmitry Zhelezov (2011-2016): Licentiate thesis, Ph.D. thesis

Urban Larsson (2008-2013): Licentiate thesis, Ph.D. thesis

MSc students :

Edvin Wedin (2014): thesis

Urban Larsson and Jonas Knape (2004): thesis

Dennis Eriksson (2004): thesis

BSc students :

Mattias Danielsson, Jimmie Ekström, Jesper Johansson and Gustav Karlsson (2015): thesis

Some Random Conference Presentations

Bristol 2016

ICDCN 2016

EURO 2015

JA 2015

Summer school on social networks, Parts 1 and 2

Summer school on social networks, Part 3


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Last modified: Tue May 02 18:12:00 CET 2017

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