## Composition and decomposition of matroids and related topics |

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### Contents

Decomposition theory for arbitrary clutters | 5 |

Examples | 10 |

Clutters with only finite members | 13 |

20 other sections not shown

### Common terms and phrases

1-isomorphism theorem 2-isomorphic 3-connected Assume basepoint bijection Boolean function called circuit Cj U C2 clearly cleavage units closed sets closed under composition closure operator clutter decomposition clutter Q collection completely decomposable component supports contradiction corollary decomposition of type definition denote direct sum directed graph disjoint example exists finite member finite set flap follows from theorem given Gj and G Hence i-committee i-quotients ieK 1 i^K implies indecomposable independent sets intersection isomorphism Let Q,f loop Math maximal committees maximum flow problem minimal multiple edges non-pointed composition non-separable matroids nonempty nontrivial sum partition path clutter pointed decomposition polygon matroids Proof proposition 3.2 prove Q Theorem quotient series reduction series-parallel series-parallel networks subsets Suppose theorem 2.1 theorem follows theorem II.5.5 transversal matroids Tutte vector spaces Zorn's lemma