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

*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 |

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 |

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