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- Dr Bridget Webb

Bridget's undergraduate and postgraduate studies were at UEA (BSc in Chemistry and Mathematics and PhD in Pure Mathematics). She joined the Open University in 1995 as a lecturer in Pure Maths, after a tutorship at Exeter University.

Bridget's research interests lie in the overlap of design theory and graph theory, where her interest in the symmetry of objects also leads to the study of automorphisms and permutation groups. Most of her research falls under the following three headings:

- Infinite designs
- Latin squares
- Combinatorial designs.

**Infinite designs**

Most work on design theory has an implicit (if not explicit) assumption of finiteness; removing this assumption leads to topics in infinite design theory, which, although part of set theory, is very combinatorial in nature. Infinite designs are particularly interesting because many ideas and techniques from finite design theory may be applied with only minor modifications where necessary, yet in other ways they behave very differently to finite designs. Bridget has published several papers on infinite designs, including one, written jointly with Prof. Peter Cameron (QMUL), that gives the definitive definition.

**Latin squares**

Latin squares are ubiquous structures which have recently gained much public interest through the popularity of Sudoku, which are one particular type of Latin square. Despite centuries of study, there are still surprisingly many basic problems remaining unanswered.

**Combinatorial designs**

Work in design theory includes research on permutations and automorphisms of designs, configurations in designs, Steinr triple systems and graph decompositions.

Current work involves countably infinite homogeneous Steiner triple systems and subsystems of Netto triple systems.

Name | Type | Parent Unit |
---|---|---|

Pure Maths: Combinatorics Research Group | Group | Faculty of Mathematics, Computing and Technology |

Role | Start date | End date | Funding source |
---|---|---|---|

Lead | 01 Jan 2015 | 31 May 2015 | EPSRC Engineering and Physical Sciences Research Council |

The overarching aim of this proposal is to make significant progress towards classifying homogeneous and set-homogeneous Steiner triple systems. In doing so, it will not only investigate possible amalgamation classes of Steiner triple systems, but will also investigate the subgroup structure of two classes of finite designs. Another aspect of this proposal is the decomposition of infinite circulant graphs into infinite Hamiltonian paths which builds on previous work by Webb and the researchers at The University of Queensland. |

Countable homogeneous Steiner triple systems avoiding
specified subsystems (2021-05)

Horsley, Daniel and Webb, Bridget S.

Journal of Combinatorial Theory, Series A, 180, Article 105434

On Hamilton decompositions of infinite circulant graphs (2018-07)

Bryant, Darryn; Herke, Sarada; Maenhaut, Barbara and Webb, Bridget S.

Journal of Graph Theory, 88(3) (pp. 434-448)

Small Partial Latin Squares that Cannot be Embedded in a Cayley Table (2017)

Wanless, Ian M. and Webb, Bridget S.

Australasian Journal of Combinatorics, 67(2) (pp. 352-363)

Resolvability of infinite designs (2014-04-30)

Danziger, Peter; Horsley, Daniel and Webb, Bridget S.

Journal of Combinatorial Theory, Series A, 123(1) (pp. 73-85)

Perfect countably infinite Steiner triple systems (2012-10)

Cameron, Peter and Webb, Bridget

Australasian Journal of Combinatorics, 54 (pp. 273-278)

Monogamous latin squares (2011-12-03)

Danziger, Peter; Wanless, Ian M. and Webb, Bridget S.

Journal of Combinatorial Theory, Series A, 118(3) (pp. 796-807)

On sparse countably infinite Steiner triple systems (2010)

Chicot, K. M.; Grannell, M. J.; Griggs, T. S. and Webb, B. S.

Journal of Combinatorial Designs, 18(2) (pp. 115-122)

Subsquare-free Latin squares of odd order (2007-01)

Maenhaut, Barbara; Wanless, Ian M. and Webb, Bridget S.

European Journal of Combinatorics, 28(1) (pp. 322-336)

The Existence of latin squares without orthogonal mates (2006-07)

Wanless, Ian M. and Webb, Bridget S.

Designs, Codes and Cryptography, 40(1) (pp. 131-135)

Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves (2004-07-06)

Bryant, Darryn; Maenhaut, Barbara; Quinn, Kathleen and Webb, Bridget S.

Discrete Mathematics, 284(1-3) (pp. 83-95)

What is an infinite design? (2002-02)

Cameron, Peter J. and Webb, Bridget S.

Journal of Combinatorial Designs, 10(2) (pp. 79-91)