# CIRCA Report 2004-2005

Introduction

CIRCA Staff

CIRCA students

Promotions and New Appointments

Grants

Research visits

Lectures

Visitors

Conferences

Publications

## Introduction

2004 and 2005 have been remarkable years for CIRCA.

We began 2004 welcoming new research staff (Murray Elder, James Mitchell, and Colva Roney-Dougal) to work on our EPSRC grants (awarded in 2003) in Symmetry and search, Computational semigroup theory and Combinatorics, and were joined during the year by Ian Miguel and Sophie Huczsynska, who chose to bring their personal research fellowships to the Centre. Building on this success, 2004 also saw the progress of our “Critical Mass” grant application (funding a substantial expansion of our multidisciplinary research over five years), from outline application (in March) through final selection panel (the most nerve-wracking presentation I’ve ever done) in December, to confirmation of our success just in time for the CIRCA Christmas party. At the same party we were also celebrating Colva’s appoinment to a lectureship and James and Sophie’s Academic Fellowships. One way and another the medium and long-term futures of interdisciplinary research and computational algebra seem very secure. 2004 also saw us entertaining visitors, organizing conferences and, of course, doing and publishing research in a wide range of areas as detailed in the rest of this report.

2005 saw the Critical Mass project actually begin in September, following a summer of recruiting support staff (John McDermott and Angie Miguel) and researchers (Alan Cain, Beth Holmes and Tom Kelsey) and trying to work out how to organize and manage the new, much expanded CIRCA. The summer also saw the Groups St Andrews conference return very successfully to St Andrews for the first time since 1989, and the success of another large grant application, this time in the European arena: “SCIEnce: Symbolic Computation Infrastructure for Europe” aims to bring together a number of groups developing (pure) mathematical software to make their systems more modern and more composable as well as promoting and supporting use of symbolic computation in European research. This project will start in April 2006. Also in 2005 our “license” from the University to exist as a Centre was renewed for another five years.

Ending my introduction to our 2002/3 “annual” report I said “The Centre enters 2004 larger and stronger than ever before, with more staff and students pursuing a broader range of exciting research projects and fruitful collaborations than ever before.” I’m delighted now to be able to say that as we enter 2006, the same claims can still be made.

**Steve Linton**

Director

March 2006

## CIRCA Staff

Steve Linton

Colin M Campbell

Ian Gent

Kevin Hammond

Sophie Huczynska

Delaram Kahrobaei

Ian Miguel

James Mitchell

John J O’Connor

Martyn Quick

Edmund F Robertson

Colva Roney-Dougal

Nik Ruškuc

### Senior Research Fellows

Beth Holmes

Tom Kelsey

### Research Fellows

Alan Cain

Peter P Campbell

Murray J Elder

Chris Jefferson

Leonid Timochouk

Vince Vatter

### Support

John McDermott

Angela Miguel

## CIRCA Students

### Ph.D.

Nelson Da Silva (2001-2005)

Erzsebet Dombi (2001-2004)

Andrew Rowley (2001-2004)

Maja Waldhausen (2001-2005)

Alan Cain (2002-2005)

Catarina Carvalho (2002-2005)

Peter Gallagher (2002-2005)

Robert Gray (2002-)

Elizabeth Kimber (2002-2005)

Dale Sutherland (2002-2005)

Morteza Jafarpour (2003-)

Peter Nightingale (2003-)

Steve Waton (2003-)

Björn Aßmann (2004-)

Robert Brignall(2004-)

Fiona Brunk (2005-)

Abram Connelly (2005-)

Yann Péresse(2005-)

### MSc

Paul von Buenau (2004-2005)

## Promotions & New Appointments

**Professor**

Steve Linton

Nik Ruškuc**Lecturer**

Sophie Huczynska

James Mitchell

Colva Roney-Dougal

Ian Miguel**Senior Research Fellow**

Beth Holmes

Tom Kelsey**Research Fellow**

Alan Cain

Chris Jefferson

Vince Vatter**Support**

John McDermott

Angela Miguel

## Grants

### Major New Grants in 2004 and 2005:

*Multidisciplinary Critical Mass in Computational Algebra and Applications*(2005-2010), EPSRC, £1,098,897

Linton, SA, Gent, IP, Miguel, I, Ruskuc, N, Quick, M, Robertson, E, Mackenzie, A, Leonhardt, U.

The problem addressed by this proposal is the development, implementation and especially the application of algorithms for computing in and with, algebraic objects such as groups, rings and monoids, that is, to compute with symmetry in its most general sense.

There are exciting interdisciplinary and multidisciplinary challenges at three stages of this: the development of new algorithms; the design of a system to allow them to be effectively implemented and combined; and their application to problems either in mathematics, or in a separate target discipline such as artificial intelligence or solid-state physics.

*SCIEnce: Symbolic Computation Infrastructure for Europe*(2006-2011), EC 6th Framework Programme, €3,200,000 overall, €726,000 at St Andrews

Linton, S. Hammond, K

We propose an integrated programme to address the fragmentation of Europe’s symbolic computation software infrastructure. This is vital infrastructure for research in a wide range of scientific disciplines, and European groups have developed many leading systems which are widely used in research, but are not composable, duplicate development effort and are failing to track relevant developments in underpinning Computer Science. We will address these issues by jointly undertaking a program of networking, software development and research, complemented by a programme of trans-national access to the world-leading Centre of Expertise at RISC-Linz.

### Complete List of Current CIRCA Grants

- EC: SCIEnce: Symbolic Computation Infrastructure for Europe. Linton, S. Hammond, K. (2006-2011)
- EPSRC: Multidisciplinary Critical Mass in Computational Algebra and Applications. Linton, SA, Gent, IP, Miguel, I, Ruskuc, N, Quick, M, Robertson, E, Mackenzie, A, Leonhardt, U. (2005-2010)
- EPSRC/Royal Academy of Engineering: An Automated Constraint Modelling Assistant. Miguel, I. Research Fellowship. (2004-2009)
- Royal Society Dorothy Hodgkin Fellowship. Huczynska, S. (2004-2008)
- Royal Society Dorothy Hodgkin Fellowship. Holmes, P.E. (2003-2007)
- EPSRC: Applications of Automata and Languages in the Theory of Pattern Classes of Permutations. Ruskuc, N, Linton, SA, Robertson, EF. (2004-2007)
- EPSRC: Refinement-Driven Transformation for Effective Automated Constraint Modelling. Miguel, I. & Gent, IP. (2006-2009)
- EPSRC: Semigroups and Monoids in GAP. Ruskuc, N, Linton, SA, Robertson, EF. (2004-2006)
- EPSRC: Symmetry and Search Network. Linton, SA, Smith, BM, Melham, TF, Gent, IP, Fox, M, Kelsey, TW. (2004-2007)
- EPSRC: Symmetry and Inference, Linton, SA, and Gent, IP. (2003-2006)
- EPSRC: Computational Algebra for Commodity Parallel Machines, Hammond, K, Linton, SA. (2003-2006)
- EPSRC/Microsoft: CASE for New Academics Grant, Miguel, I. (2006-2009)
- EPSRC: Academic Fellowship. Mitchell, J. (2005-2010)

## Research Visits

### 2004

CMC: NUI Galway, Ireland

DK: Institute des Hautes Etudes Scientifique, Bures-sur-Yvette, France; University of Warwick; Institute for studies in theoretical physics and mathematics, Tehran, Iran.

EFR: Aachen, Germany; NUI, Galway, Ireland; Miskolc, Hungary

NR: Otago University, Dunedin, New Zealand; University of Cambridge; NUI Galway, Ireland

SL: Otago, Aukland, Perth, Australia

### 2005

DK: The Royal Institute of Technology in Stockholm, Sweden

CJ: Cork Constraints Computation Centre (4C), University College Cork, Ireland

DK: EPFL (Switzerland); IPM – Institute for studies in Theoretical Physics and Mathematics, Tehran, Iran; University of Geneva, Switzerland; CRM, Barcelona, Spain; KTH, Stockholm, Sweden; Oxford University, University of Glasgow, Queens Belfast University, Heriot-Watt University, Edinburgh

IJM: Imperial College, London

JM: CAUL, Lisbon; Technical University of Wroclaw, Poland; University of Louisville, USA

CRD: University of Sydney, Australia; University of Warwick

NR: Dunedin, New Zealand

CMC: NUI Galway, Ireland

EFR: NUI Galway, Ireland

## Lectures

### 2004

CMC: Braunschweig, Germany

SH: University of Edinburgh

DK: IHES Mathematics seminar, Institute des Hautes Etudes Scientifiques, Bures-sur-Yvette, France; New York Logic Workshop, Graduate Centre, CUNY; Ecole Normale Superieure de Lyon, France; Institute for studies in Theoretical Physics and Mathematics, Tehran, Iran (3 lectures); Sharif University of Technology, Tehran, Iran; Rutgers University Group Theory seminar, New Brunswick, USA; Courant Institute of Mathematical Sciences, New York University; Cryptography Seminar, University of Warwick.

EFR: University of Miskolc, Hungary; NUI Galway, Ireland

NR: Cambridge Combinatorics seminar

IJM: University of Nottingham, University of Edinburgh

IPG: CP2004 (tutorial talk)

### 2005

IJM: Seminar, Imperial College, London

CJ: Seminar, 4C, University College Cork

MQ: University of Glasgow, University of Manchester

DK: IPM – Institure for studies in Theoretical Physics and Mathematics, Tehran, Iran; University of Geneva, Switzerland; CRM – Centre de Recerca Matematica, Barcelona, Spain; Isaac Newton Institure for Mathematical Sciences, Cambridge; Kungl. Tekniska Hogskolan Matematiska Institutioned, Stockholm, Sweden; Ecole Polytechnique Federale de Lausanne, Switzerland

CRD: MAGMA workshop on group theory and algebraic geometry, University of Warwick

NR: CATS, ACSW Newcastle, NSW, Australia; International Algebraic Conference, Ekaterinburg, Russia.

CMC: NUI Galway, Ireland

AC: University of Edinburgh; Heriot Watt, Edinburgh

EFR: North Eastern Geometric Group Theory Seminar

## Visitors

### 2004

Michael Albert (University of Otago, Dunedin, New Zealand)

Rick Thomas (University of Leicester)

Walter Neumann (Columbia University, USA)

Andrew Rechnitzer (University of Melbourne, Australia)

George Havas (University of Queensland, Australia)

Andrew Fish (University of Brighton)

Derek Holt (University of Warwick)

Chris Jefferson (University of York)

Patrick Prosser (University of Glasgow)

Karen Petrie (University of Huddersfield)

Barbara Smith (University of Huddersfield)

### 2005

Katrin Gehles (University. of Glasgow)

Jorge Andre (CAUL, Lisbon, Portugal)

Vince Vatter (Rutgers University, USA)

Alan Frisch (University of York)

Chris Jefferson (University of York)

Karen Petrie (Cork Constraints Computation Centre (4C), Ireland)

Derek Holt (University of Warwick)

John Bray (Queen Mary, University of London)

Patrick Prosser (University of Glasgow)

E. Breuillard (IHES-Institute des Hautes Etudes Scientifiques, France)

M. Morayne (University of Wroclaw, Poland)

U. Darji (University of Louisville, USA)

J. Truss (University of Leeds)

S. Murray (T U Eindhoven, The Netherlands)

V. Gould (University of York)

Barbara Smith (Cork Constraints Computation Centre (4C), Ireland)

## Conferences Organised

**SymNet Workshop (2004)**

The first Symmetry & Search Network (SymNet) Summer School was held at St Andrews from Monday 28th June to Friday 22nd July 2004. The topics covered included: Symmetry in Planning, Symmetry breaking in Constraint Programming, an introduction to ECLiPSe, an introduction to Computational Group Theory, GAP programming, an introduction to Boolean Satisfiability, Model Checking – symmetry detection in models of concurrent systems, Graph Theory, Design Theory, and Proof Complexity – symmetry gaps and complexity. The speakers were: Derek Long, Barbara Smith, Ian Gent, Karen Petrie, Warwick Harvey, Steve Linton, Igor Markov, Alastair Donaldson, Brendan McKay, Jan Degraer, Leonard Soicher, and Soren Riis.

**SAT (2005)**

From the proceedings of SAT 2005:

The 8th International Conference on Theory and Applications of Satisfiablility Testing was held in St Andrews from June 19th-June 23rd 2005. The 2005 SAT Solver Competition and 2005 QBF Solver Evaluation took place along with the conference. SAT 2005 provided an international forum for the most recent research on the satisfiability problem (SAT). SAT is the classic problem of determining whether or not a propositional formula has a satisfying truth assignment. It was the first problem shown by Cook to be NP-complete. Despite its seemingly specialized nature, satisfiability testinghas proved to be extremely useful in a wide range of different disciplines, from from a practical as well as a theoretical point of view. For example, work on SAT continues to provide insight into various fundamental problems in computation, and SAT solving technology has advanced to the poitn where it has become the most effective way of solving a number of practical problems.

The SAT series of conferences are multidisciplinary conferences intended to bring together researchers from various disciplines who are interested in SAT. Topics of interest include , but are not limited to: proof systems and proof complexity; search algorithms and heuristics; analysis of algorithms; theories beyond the propositional; hard instances and random formulae; problem encodings; industrial applications; solvers and other tools.

**SARA (2005)**

From the proceedings of SARA 2005:

The 6th **S**ymposium on **A**bstraction, **R**eformulation and **A**pproximation 2005 was held in Airth Castle near Falkirk from July 26th to July 29th 2005. This was just prior to the IJCAI 2005 conference in Edinburgh. This was the first time that the symposium was held in Europe.

Abstractions, reformulations and approximations (AR&A) have found applications in a variety of disciplines and problems, including constraint satisfaction, design, diagnosis, machine learning, planning, qualitative reasoning, scheduling, resource allocation and theorem proving, but are also deeply rooted in philisophy and cognitive science. The papers SARA 2005 capture a cross-section of the various facets of the fieldand of its applications. One of the primary uses of AR&A is oriented to overcome computational intractability. AR&A techniques, however, have also proved useful for knowledge aquisition, explanation and other applications.

**Groups St Andrews (2005)**

Groups St Andrews 2005 ran from 30th July – 6th August and was held in St Andrews. This conference was the 7th in the series. The conference aims to cover all aspects of group theory. Lecture courses were given that aimed to be accessible to postgraduate students, postdoctoral fellows, and researchers in all areas of group theory. The principal speakers were:

- Peter J Cameron (Queen Mary, University of London)
*Aspects of infinite permutation groups* - Rostislav I Grigorchuk (Texas A&M, USA)
*On self-similarity and branching in group theory* - John C Meakin (Nebraska-Lincoln, USA)
*Interactions between group theory and semi-group theory* - Akos Seress (Ohio State, USA)
*Graphs, automorphisms and product action*

**Scottish Algebra Day (2005)**

Scottish Algebra Day 2005 was held at Edinburgh University on the 6th May 2005. It involved talks on “Representing words in automorphisms groups” by John Truss (Leeds), “The geometry monoid of an algebriac law” by Patrick Dehornoy (Caen, France), “Localization theorems in modern algebra” by Dmitry Rumynin (Warwick), and “Algebras defined by homogeneous semigroup relations” by Jan Okninski (Warsaw, Poland).

**The Copson Lecture (2005)**

The first Copson lecture was held in November 2005. The school of Mathematics and Statistics received a generous endowment from the Copson family to fund a bi-annual lecture in memory of Professor Edward Copson, a former Regis Professor of Mathematics here at St Andrews, and Mrs Beatrice Copson. The Copson lecture will alternate with the Curle lecture, which was last held in 2004. The speaker for this first Copson lecture was Marcus du Sautoy (University of Oxford). The title of the lecture was “Music of the Primes”.

## Publications

### 2004

- Banks, D, Linton, S A, Stockmeyer, P: Counting Cases in Substitope Algorithms
*IEEE Transactions on Visualization and Computer Graphics***10, 4,**pp 371-384. 2004. - Boulton, R J, Gottliebsen, H, Hardy, R, Kelsey, T W, and Martin, U: Design Verification for Control Engineering.
*Lecture Notes in Computer Science***2999**, Proc. 4th International Conference on Integrated Formal Methods (IFM 2004), Canterbury, UK, pp 21-35. Springer, 2004. - Brooksbank, P, Qin, H, Robertson, E F and Seresse, A: On Dowling geometries of Infinite groups.
*Journal of Combinatorial Theory Series A*,**108**, 155-158 - Campbell, C M and Campbell, P P: On the minimal length of semigroup presentations,
*Novi Sad Journal of Mathematics***34**, 17-26. - Campbell, C M, Campbell, P P, Doostie, H and Robertson, E F: Fibonacci lengths for certain metacyclic groups,
*Algebra Colloquium***11**, 215-222. - Campbell, C M, Campbell, P P, Doostie, H and Robertson, E F: On the Fibonacci length of powers of dihedral groups,
*Applications of Fibonacci Numbers***9**, 69-85, (ed F T Howard), Kluwer, Dordrecht. - Campbell, C M, Havas, G, Ramsay, C and Robertson, E F: Nice efficient presentations for all small simple groups and their covers,
*LMS Journal of Computational Mathematics***7**, 266-283. - Delgado, M, Linton, S A, Morais, J: Automata.
*gap-system.org.*2004. - Frisch, A M, Jefferson, C and Miguel, I: Symmetry breaking as a Prelude to Implied Constraints: A Constraint Modelling Pattern.
*Proceedings of the 16th European Conference on Artificial Intelligence*, pages 171-175, 2004. - Frisch, A M, Jefferson, C, Martinez-Hernandez, B and Miguel I: Generating Effective Constraint Programs: An Application of Automated Reasoning. Proceedings of the 11th Workshop on Automated Reasoning, 2004.
- Frisch, A M, Jefferson, C, Martinez-Hernandez, B and Miguel I: The Rules of Modelling: Towards Automatic Generation of Constraint Programs.
*Proceedings of the 3rd International Workshop on Modelling and Reformulating Constraint Satisfaction Problems*, 2004. - Gent, I P and Rowley, A G D: Encoding Connect-4 using Quantified Boolean Formulae.
*Proc.of the 2nd International Workshop on Modelling and Reformulating Constraint Satisfaction Problems*, Kinsale, Ireland, Frisch, AM (ed), pp 78-93. 2004. - Gent, I P, McDonald, I, Miguel, I and Smith, B M: Approaches to Conditional Symmetry Breaking.
*Proceedings of the 4th International Workshop on Symmetry and Constraint Satisfaction Problems*, 2004. - Gent, I P, Nightingale, P and Rowley, A G D: Encoding Quantified CSPs as Quantified Boolean Formulae.
*Proc. 16th European Conference on Artificial Intelligence (ECAI 2004)*, Valencia, Spain. 2004. - Gent, I P and Nightingale, P: A New Encoding of AllDifferent into SAT.
*Proc. 3rd International Workshop on Modelling and Reformulating Constraint Satisfaction Problems*, CP2004, Toronto, Canada, Frisch, AM, Miguel, I (eds). 2004 - Hnich, B, Kiziltan, Z, Miguel, I and Walsh, T: Hybrid Modelling for Robust Solving.
*Annals of Operations Research***130**(1-4), pages 19-39, 2004. - Kelsey, T, Linton, S A, Roney-Dougal, C M: New Developments in Symmetry Breaking in Search Using Computational Group Theory.
*Proc. 7th International Conference on Artificial Intelligence and Symbolic Computation (AISC 2004)*. Springer LNAI. 2004. - Linton, S A: Finding the Smallest Image of a Set.
*Proc. International Symposium on Symbolic and Algebraic Computation (ISSAC 2004)*, Santander, Spain. 2004. - Miguel, I: Dynamic Flexible Constraint Satisfaction and its Application to AI Planning. Springer Distinguished Dissertations Series, 2004.
- O’Connor, J J and Robertson, E F: Isaac Barrow and William Ernest Johnson
*Biographical Dictionary of British Economists*, (ed D Rutherford), Thoemmes Continuum. - O’Connor, J J and Robertson, E F: Obituary: David Allan Spence,
*Australian Mathematical Society Gazette***31(1)**, 58-59. - Quick, M: Probabilistic generation of wreath products of non-abelian finite simple groups,
*Communications in Algebra***32**, 4753-4768. - Roney-Dougal, C M, Gent, I P, Kelsey, T W, and Linton, S A: Tractable Symmetry Breaking using Restricted Search Trees.
*Proc. 16th European Conference on Artificial Intelligence (ECAI 2004)*, Valencia, Spain. 2004. - Smith, B M, Petrie, K E and Gent I P: Models and Symmetry Breaking for Peaceable Armies of Queens.
*Proc. International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimisation Problems (CP-AI-OR’04)*, Nice, France. 2004. - Tarim, S A and Miguel, I: Echelon Stock Formulation of Arborescent Distribution Systems: An Application to the Wagner-Whitin Problem.
*Proceedings of the International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimisation Problems (CPAIOR)*,**LNCS 3011**, 2004. - Wallace, W H B, Kelsey, T W: Ovarian Reserve and Reproductive Age may be Determined from Measurement of Ovarian Volume by Transvaginal Sonography.
*Human Reproduction***19, 7,**pp 1-6. 2004.

### 2005

- Albert, M H, Linton S A and Ruskuc, N: The Insertion Encoding of Permutations,
*Electron. J. Combinat.***12**, R47. - Araujo, J and Mitchell, J D: ‘An elementary proof that every singular nxn matrix is a product of idempotents’,
*Amer. Math. Monthly***112**(2005) 641-645. - Bartlett, M, Frisch, A M , Hamadi, Y, Miguel, I, Tarim, S A and Unsworth C: The Temporal Knapsack Problem and Its Solution.
*Proceedings of the 2nd International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR)*, 34-48, 2005. - Campbell, C M and Campbell, P P: The Fibonacci length of certain centro-polyhedral groups,
*J. Appl. Math. Comput.***19**, 231 – 240. - Descalco, L and Ruskuc, N: Subsemigroups of the bicyclic monoid,
*Internat. J. Algebra Comput.***15**, 37-57. - Dombi, E R, Gilbert, N D and Ruskuc, N: Finite presentability of HNN extensions of inverse semigroups,
*Internat. J. Algebra Comput.***15**, 423-436. - Frisch, A M, Hnich, B, Miguel, I, Smith, B M and Walsh, T: Transforming and Refining Abstract Constraint Specifications.
*Proceedings of the 6th International Symposium on Abstraction, Reformulation and Approximation (SARA)*,**LNAI 3607**, 76-91, 2005 - Frisch, A M, Jefferson, C, Martinez-Hernandez, B and Miguel, I: The Rules of Constraint Modelling.
*Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI)*, 109-116, 2005. - Frisch, A M, Grum, M, Jefferson, C, Martinez-Hernandez, B and Miguel, I: The Essence of ESSENCE: A Constraint Language for Specifying Combinatorial Problems.
*Proceedings of the 4th International Workshop on Modelling and Reformulating Constraint Satisfaction Problems*, 73-88, 2005 - Frisch, A M, Jefferson, C, Martinez-Hernandez, B and Miguel, I: The Rules of Constraint Modelling: An Overview.
*Proceedings of the 12th Workshop on Automnated Reasoning*, 2005 - Gallagher, P and Ruskuc, N: Finitary power semigroups of infinite groups are not finitely generated,
*Bull. London Math. Soc.***37**, 386-390. - Gallagher, P and Ruskuc, N: Generation of diagonal acts of some semigroups of transformations and relations,
*Bull. Austral. Math. Soc.***72**, 139-146. - Gent, I P, Kelsey, T, Linton, S A, McDonald, I, Miguel, I and Smith, B M: Conditional Symmetry Breaking.
*Proceedings of the 11th International Conference on Principles and Practice of Constraint Programming (CP 2005)*, 256-270, Springer Verlag. 2005 - Gent, I P, Kelsey, T, Linton, S A, Roney-Dougal, C M: Symmetry and Consistency.
*Proceedings of the 11th International Conference on Principles and Practice of Constraint Programming (CP 2005)*271-285. Springer Verlag. 2005 - Gent, I P, Nightingale, P, and Stergiou, K: QCSP-Solve: A solver for quantified constraint satisfaction problems.
*Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI)*, 138-143, 2005. - Gent, I P and Rowley, A G D: Local and global complete solution learning methods for QBF.
*Lecture Notes in Computer Science***3569**, 91-106. Springer, 2005. - Gottliebsen, H, Kelsey, T, Martin, U: Hidden Verification for Computational Mathematics
*Journal of Symbolic Computation,*pp 539-567. 2005. - Havas, G and Robertson, E F: The F^{a,b,c} Conjecture, I,
*Irish Math. Soc. Bulletin***56**75-80, 2005. - Kahrobaei, D: A Simple Proof of a Theorem of Karrass and Solitar
*Contemporary Mathematics*,**372**107-108, 2005 - Kahrobaei, D, Bhutani, K and Khan, B: A Graphic Generalization of Arithmetic
*Electronic Journal of Combinatorial Number Theory*. 2005 - Miguel, I and Shen, Q: Exhibiting the Behaviour of Time-Delayed Systems via an Extension to Qualitative Simulation
*IEEE Transactions on Systems, Man and Cybernetics (Part A)***35(2)**, 298-305, 2005 - O’Connor, J J and Robertson, E F: The MacTutor History of Mathematics Archive.
*http://www-history.mcs.st-and.ac.uk/history/* - Roney-Dougal, C M: The primitive groups of degree less than 2500.,
*J.Algebra.***292**, 154-183. - Roney-Dougal, C and Holt, D: Constructing maximal subgroups of classical groups.
*LMS Journal of Computational Mathematics*,**8**, (2005) 46-79. - Tarim, S A and Miguel, I: A Hybrid Benders’ Decomposition Method for Solving Stochastic Constraint Programs with Linear Recourse.
*Proceedings of the CSCLP 2005: Joint Annual Workshop on ERCIM/CoLogNet on Constraint Solving and Constraint Logic Programming*, 148-162, 2005 - Wallace, W H, Thomson, A B, Saran, F and Kelsey, T W: Predicting Age of Ovarian Failure After Radiation to a Field that Includes the Ovaries.
*International Journal of Radiation Oncology*Biology*Physics***62, 3,**pp 738-744. 2005.

## CIRCA Preprints

### 2004

**2004/1**

Colin M. Campbell, George Havas, Colin Ramsay, and Edmund F. Robertson, *Nice Efficient presentations for all small simple groups and their covers***2004/2**

Colva M. Roney-Dougal, *Conjugacy of subgroups of the general linear group***2004/3**

Colva M. Roney-Dougal, Ian Gent, Tom Kelsey, and Steve Linton, *Tractable symmetry breaking using restricted search trees***2004/4**

Steve Linton, *Finding the smallest image of a set***2004/5**

Derek F. Holt and Colva M. Roney-Dougal, *Constructing maximal subgroups of classical groups***2004/6**

Tom Kelsey, Steve Linton, and Colva M. Roney-Dougal, *New developments in symmetry breaking in search using computational group theory***2004/7**

Peter Brooksbank, Hongxun Qin, Edmund Robertson, and Akos Seress, *On Dowling Geometries of Infinite Groups***2004/8**

Colin M. Campbell, and Peter P. Campbell, *The Fibonacci lengths of binary polyhedral groups and related groups***2004/9**

Martyn Quick, *Maximal complements in finite groups***2004/10**

Peter P. Campbell, *Wall numbers for the first 100,001 prime numbers***2004/11**

Sophie Huczynska and Nik Ruskuc, *Pattern classes of permutations via bijections between linearly ordered sets***2004/12**

Colva M. Roney-Dougal, *The primitive groups of degree less than 2500***2004/13**

Murray Elder, *Pattern avoiding permutations are context-sensitive*

### 2005

**2005/1**

Martyn Quick, *Groups whose proper quotients are virtually abelian*

**2005/2**

Björn Aßmann, *Algorithmic use of the Mal’cev correspondence*

**2005/3**

George Havas and Edmund F Robertson, *The F ^{a,b,c} conjecture is true, I*

**2005/4**

Steve Linton and Colva M Roney-Dougal,

*Identifying geometries preserved by matrix groups*

**2005/5**

George Havas, Edmund F Robertson and Dale C Sutherland,

*The F*

^{a,b,c}conjecture is true, II**2005/6**

James D Mitchell , Yann Péresse and Martyn Quick,

*Generating Sequences of Functions*