## Higher Combinatorics: Proceedings of the NATO Advanced Study Institute held in Berlin (West Germany), September 1–10, 1976It is general consensus that Combinatorics has developed into a full-fledged mathematical discipline whose beginnings as a charming pastime have long since been left behind and whose great signifi cance for other branches of both pure and applied mathematics is only beginning to be realized. The last ten years have witnessed a tremendous outburst of activity both in relatively new fields such as Coding Theory and the Theory of Matroids as well as in' more time honored endeavors such as Generating Functions and the Inver sion Calculus. Although the number of text books on these subjects is slowly increasing, there is also a great need for up-to-date surveys of the main lines of research designed to aid the beginner and serve as a reference for the expert. It was the aim of the Advanced Study Institute "Higher Combinatorics" in Berlin, 1976, to help fulfill this need. There were five sections: I. Counting Theory, II. Combinatorial Set Theory and Order Theory, III. Matroids, IV. Designs and V. Groups and Coding Theory, with three principal lecturers in each section. Expanded versions of most lectures form the contents of this book. The Institute was designed to offer, especially to young researchers, a comprehen sive picture of the most interesting developments currently under way. It is hoped that these proceedings will serve the same purpose for a wider audience. |

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### Contents

DISTRIBUTIONS EULERIENNES ET MAHONIENNES SUR LE GROUPE | 27 |

COHENMACAULAY COMPLEXES | 48 |

ACYCLIC ORIENTATIONS | 65 |

ASPECTS OF FINITE LATTICES | 79 |

GEOMETRIES ASSOCIATED WITH PARTIALLY ORDERED SETS | 105 |

MATROIDS AS THE STUDY OF GEOMETRICAL CONFIGURATIONS | 133 |

PARTITIONS OF x2 AND OTHER TOPICS | 178 |

EDGE DECOMPOSITIONS OF COLORED GRAPHS | 200 |

PERMUTATION GROUPS ON UNORDERED SETS | 217 |

CODES AND DESIGNS | 240 |

### Other editions - View all

Higher Combinatorics: Proceedings of the NATO Advanced Study Institute held ... M. Aigner No preview available - 2011 |

### Common terms and phrases

0-sequence Aigner algebraic Amer biplane block chain partition characterization Cohen-Macaulay colour combinatorial geometry complete class configuration construction contains cyclic flats defined denoted Desargues Desargues configuration Dilworth truncation distributive lattices elements eulérienne example finite lattice finite partially ordered free matroid function Germany Gorenstein graph group G h-vector Hence Higher Combinatorics hyperplane identity IMAJ incidence incidence matrix indep independent induced infinite Inst integers IRISE irreducible isomorphic J.A. Thas lemma linear lines Math matrix matroid join maximal arc modular cut modular lattices nombre number of partitions obtain parallel partial geometries partial lattice partially ordered set perfect codes permutation group plane of order points polynomial poset primitive Proc projective plane proof q-analog quadrangle with parameters rank regular Reidel Publishing Company relation representation resp restriction result simplicial Steiner system strict gammoids strong map subquadrangle subset subspace t-transitive theory transitive transversal matroids unique Univ vector space weak maps