## Higher combinatorics: proceedings of the NATO Advanced Study Institute held in Berlin (West Germany), September 1-10, 1976 |

### From inside the book

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Page 119

In particular, X is a

of M*. It is not difficult to check that a matroid M on a given set is completely

determined by specifying the collection F(M) of all its

their ...

In particular, X is a

**cyclic flat**of M if and only if the complement of X is a**cyclic flat**of M*. It is not difficult to check that a matroid M on a given set is completely

determined by specifying the collection F(M) of all its

**cyclic flats**together withtheir ...

Page 120

F(M) has a natural lattice structure, with FvG the usual join of flats, i.e. the span pt

FuG, and FaG the union of all the circuits ... as was proved by Brualdi and Mason

[10] but also imposes a restriction on the way the

F(M) has a natural lattice structure, with FvG the usual join of flats, i.e. the span pt

FuG, and FaG the union of all the circuits ... as was proved by Brualdi and Mason

[10] but also imposes a restriction on the way the

**cyclic flats**fit together.Page 121

of all families of cyclic sets, but, as in the case of Theorem 2, it is not difficult to

show that it is enough to consider

and require the condition only for a very restricted set of families of

of all families of cyclic sets, but, as in the case of Theorem 2, it is not difficult to

show that it is enough to consider

**cyclic flats***. In fact, it is possible to go furtherand require the condition only for a very restricted set of families of

**cyclic flats**.### What people are saying - Write a review

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### Contents

THE ROLE OF EULERIAN SERIES | 3 |

DISTRIBUTIONS EULERIENNES ET MAHONIENNES SUR LE GROUPE | 27 |

COHENMACAULAY COMPLEXES | 48 |

Copyright | |

9 other sections not shown

### Other editions - View all

Higher Combinatorics: Proceedings of the NATO Advanced Study Institute held ... M. Aigner Limited preview - 2012 |

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

Higher Combinatorics: Proceedings of the NATO Advanced Study Institute held ... M. Aigner No preview available - 1977 |

### Common terms and phrases

Aigner algebraic biplane block chain partition characterization Cohen-Macaulay colour combinatorial geometry complete class configuration construction contains cyclic flats defined denoted 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 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 nombres number of partitions O-sequence obtain parallel parameters s,t 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 relation representation resp restriction result Rogers-Ramanujan identities S.E. Payne simplicial Steiner system strict gammoids strong map subquadrangle subset subspace t-transitive transitive transversal matroids unique Univ V-code vector space weak maps