## Surveys in Combinatorics 2003The British Combinatorial Conference is held every two years and is a key event for mathematicians worldwide working in combinatorics. In June 2003 the conference was held at the University of Wales, Bangor. The papers contained here are surveys contributed by the invited speakers and are of the high quality that befits the event. There is also a tribute to Bill Tutte who had a long-standing association with the BCC. The papers cover topics currently attracting significant research interest as well as some less traditional areas such as the combinatorics of protecting digital content. They will form an excellent resource for established researchers as well as graduate students who will find much here to inspire future work. |

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### Contents

WT Tutte 19172002 | 1 |

Decompositions of complete graphs embedding partial edgecolourings and the method of amalgamations | 7 |

Combinatorial schemes for protecting digital content | 43 |

Matroids and Coxeter groups | 79 |

Defining sets in combinatorics a survey | 115 |

Finite projective planes with a large abelian group | 175 |

Algorithmic aspects of graph homomorphisms | 239 |

Counting lattice triangulations | 277 |

Partition regular equations | 309 |

KostkaFoulkes polynomials and Macdonald spherical functions | 325 |

### Common terms and phrases

abelian group affine difference set algebraic algorithm amalgamations Anne Penfold bipartite blocks bound codewords collineation group colour class colouring problem combinatorial complete graph Comput conjecture contains Corollary corresponding Coxeter group Coxeter matroids cycle cyclic decomposition denote desarguesian desarguesian planes desc(X Discrete Math edge-colouring edges element embedding example exists finite flag matroid forcing number frameproof codes geometry graph G group G group ring Hilton homomorphism hyperovals integer intersection isomorphic Jungnickel k-IPP code Kostka-Foulkes polynomials latin square Lemma loops matroid matroid polytope maximal minimal defining set multiplier one-factors pair partial latin square partition regular permutation planar difference set plane of order polynomial polytope precoloured projective plane proof proved relative difference sets result Section semifield semimodular lattice semiplane smallest defining set Steiner triple systems subgraph subgroup subset symmetric symplectic matroid Theorem theory traitor tracing treewidth unimodular triangulations unique vertex vertices