Combinatorial GeometriesThis book is a continuation of Theory of Matroids (also edited by Neil White), and again consists of a series of related surveys that have been contributed by authorities in the area. The volume begins with three chapters on coordinatisations, followed by one on matching theory. The next two deal with transversal and simplicial matroids. These are followed by studies of the important matroid invariants. The final chapter deals with matroids in combinatorial optimisation, a topic of much current interest. The whole volume has been carefully edited to ensure a uniform style and notation throughout, and to make a work that can be used as a reference or as an introductory textbook for graduate students or non-specialists. |
Contents
1 | 20 |
Binary Matroids J C Fournier | 28 |
Unimodular Matroids Neil White | 40 |
Transversal Matroids Richard A Brualdi | 72 |
The Möbius Function and the Characteristic Polynomial | 114 |
Whitney Numbers Martin Aigner | 139 |
Matroids in Combinatorial Optimization Ulrich Faigle | 161 |
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Common terms and phrases
A₁ algebraic b₁ b₂ base orderable basis of M(S binary matroids bipartite graph Brualdi Brylawski C₁ C₂ characteristic polynomial chromatic polynomial circuits cocircuit cographic columns Combinatorial Geometries construction contains coordinatizable coordinatization copoints Corollary Crapo cyclic flats define denote disjoint dual edges Edmonds elements entries equivalent example exists field follows geometric lattice graphic matroids greedy algorithm ground set rank Hence Homotopy Theorem hyperplanes independent set induction Ingleton integral matroid isomorphic lattice of rank Lemma Let M(S Lindström M₁ M₂ Math matrix matroid M(S matroid of rank matroid theory maximal presentation Möbius function modular nodes non-zero obtain optimization problem partial transversal path presentation of M(S Prove respect Rota S₁ satisfies set rank function simplicial matroids spanning strict Menger matroids submodular function submodular system subspace supermodular Suppose Theorem transversal matroid Tutte Tutte's U₁ unimodular matroids vector space vertex vertices Whitney numbers zonotope