## Combinatorial TheoryIncludes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs. |

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### Contents

Permutations and Combinations | 1 |

Inversion Formulae | 8 |

Generating Functions and Recursions | 20 |

Partitions | 31 |

Distinct Representatives | 48 |

Ramseys Theorem | 73 |

Some Extremal Problems | 77 |

Convex Spaces and Linear Programming | 85 |

Block Designs | 126 |

Difference Sets | 147 |

Finite Geometries | 199 |

Orthogonal Latin Squares | 222 |

General Constructions of Block Designs | 264 |

Theorems on Completion and Embedding | 336 |

Coding Theory and Block Designs | 376 |

Graphical Methods DeBruijn Sequences | 110 |

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### Common terms and phrases

arcs automorphism biplane block design Bruck-Ryser-Chowla theorem choice classes coefficients complete cycles condition construct convex cone copositive corresponding define deletion difference set distinct representatives doubly stochastic entries equation equivalent exactly once exists finite field fixed GF(p GF(q given gives graph group G H matrix Hadamard Hadamard matrix Hence hyperplane incidence matrix integers intersection l(mod Latin squares Lemma linear matrix of order modulo multiplication nonnegative nonzero objects orbit parameters partially ordered set partitions per(a permutation permutation matrix plane of order points polynomial prime power primitive root problem projective plane Proof proved quadratic form quadratic residues rational recursive relation residues modulo ri ri row and column satisfying Steiner triple system strongly regular graph subsets suppose symmetric design unique values vector whence word of weight write yields zero