Economics, Mathematics and Statistics

Cooperation, Behavioural Synchrony and Status in Social Networks

by Tamas David-Barrett

In this paper we present a new approach to modelling group coordination, based on dyadic synchronisation in a... more In this paper we present a new approach to modelling group coordination, based on dyadic synchronisation in a non-panmictic, structured network (a problem that applies widely to all species that live in medium to large groups). Using this approach, we present three models with three new theoretical results. (1) Multi-layered networks are optimal for groups that face costs associated with maintaining relationships among the members, combined with costs associated with information flow. (2) The presence of a social hierarchy can be an adaptive feature of the community: the steeper the optimal social hierarchy is, the fewer relationships group members need to have. (3) Falling communication costs lead to a less steep optimal social hierarchy in communities in which socially useful information is evenly distributed, but to an even steeper social hierarchy in groups in which socially useful information is uneven. Thus we show how, when communication is costly, cooperation can give rise to communities that are socially highly structured.

ECB Policy Response to the Euro/US Dollar Exchange Rate

by ishak demir

Maximal length parabolic subgroups in finite Coxeter groups

by Sarah Hart

Poincaré Series of Cosets in Coxeter Groups

by Sarah Hart

Zero excess and minimal length in finite coxeter groups

by Sarah Hart

Commuting involution graphs for [(A)\ tilde] n

by Sarah Hart

Involution products in finite Coxeter groups

by Sarah Hart

The case of equality in the Livingstone-Wagner Theorem

by Sarah Hart

On cosets in Coxeter groups

by Sarah Hart

Small maximal sum-free sets

by Sarah Hart

LENGTHS OF PARABOLIC SUBGROUPS IN FINITE COXETER GROUPS

by Sarah Hart

Lengths of Subsets in Coxeter Groups

by Sarah Hart

Keep Your Word: Time Varying Inflation Targets and Inflation Targeting Performance

by ishak demir

The Extent of Trade Mis-Invoicing in Turkey: Did Post-1990 Policies Matter?

by ishak demir

Generation of finite simple groups with an application to groups acting on Beauville surfaces

by Ben Fairbairn

with Kay Magaard and Christopher Parker

We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these... more We develop theorems which produce a multitude of hyperbolic triples for the finite classical groups. We apply these theorems to prove that every quasisimple group except Alt(5) and SL_2(5) is a Beauville group. In particular, we settle a conjecture of Bauer, Catanese and Grunewald which asserts that all non-abelian finite simple groups except for the alternating group Alt(5) are Beauville groups.

Some exceptional Beauville structures

by Ben Fairbairn

submitted to the Mathematische Zeitschrift. Also available on the arxiv.

We first show that every quasisimple sporadic group possesses an unmixed strongly real Beauville structure aside from... more We first show that every quasisimple sporadic group possesses an unmixed strongly real Beauville structure aside from the Mathieu groups M11 and M23 (and possibly 2B and M). To do this we give the first generic construction of objects of this kind which in princicpal may be adapted to a number of other cases. We go on to show that no almost simple sporadic group possesses a mixed Beauville structure. We then go on to use the exceptional nature of the alternating group A6 to give a strongly real Beauville structure for this group correcting an earlier error of Fuertes
and Gonzalez-Diez. In doing so we complete the classication of alternating groups that possess strongly real Beauville structures. We conclude by discussing mixed Beauville structures of the
groups A6 : 2 and A6:2^2.

New Upper Bounds on the Spreads of the Sporadic Simple Groups

by Ben Fairbairn

To appear in Communications in Algebra. Note that, compared to the version to be published, this version gives better bounds for M23 and the Baby Monster and contains an additional section giving some concluding remarks.

Let G be a group. We say that G has spread r if for any set of distinct nontrivial elements {x1, . . . , xr} ⊂ G there... more Let G be a group. We say that G has spread r if for any set of distinct nontrivial elements {x1, . . . , xr} ⊂ G there exists an element y ∈ G with the property that <xi, y> = G for every 1 ≤ i ≤ r. Few bounds on the spread of finite simple groups are known. In this paper we present improved upper bounds for the spread of many of the larger sporadic simple groups, in some cases improving on the best known upper bound by several orders of magnitude.

Recent Progress in the Symmetric Generation of Groups

by Ben Fairbairn

A survey article accepted for the proceedings of the conference `Groups St Andrews 2009'

Many groups posses highly symmetric generating sets that are naturally endowed with an underlying combinatorial... more Many groups posses highly symmetric generating sets that are naturally endowed with an underlying combinatorial structure. Such generating sets can prove to be extremely useful both theoretically in providing new existence proofs for groups and practically by providing succinct means of representing group elements. We give a survey of results obtained in the study of these symmetric generating sets. In keeping with earlier surveys on this matter, we emphasize the sporadic simple groups.

Extensions of Symmetric Generating Sets

by Ben Fairbairn

in preparation

In this paper we review existing methods of extending symmetric generating sets, namely Transitive Extensions and... more In this paper we review existing methods of extending symmetric generating sets, namely Transitive Extensions and Subset Extensions before introducing a new approach using wreath products. We proceed to give examples of this new construction, most notably for the unitary groups U_3(2^r).

Symmetric Presentations of Coxeter Groups

by Ben Fairbairn

A slightly old version of a paper submitted to the "Proceedings of the Edinburgh Mathematical Society"

We apply the techniques of symmetric generation to establish the
standard presentations of the finite simply... more We apply the techniques of symmetric generation to establish the
standard presentations of the finite simply laced irreducible finite
Coxeter groups, that is the Coxeter groups of types An, Dn and
En and show that these are naturally arrived at purely through
consideration of certain natural actions of symmetric groups. We
go on to use these techniques to provide explicit representations of these groups.