### Introduction to the Theory of Matroids - download pdf or read online

By Dr. Rabe von Randow (auth.)

ISBN-10: 3540071776

ISBN-13: 9783540071778

ISBN-10: 3642482929

ISBN-13: 9783642482922

Matroid thought has its foundation in a paper by way of H. Whitney entitled "On the summary houses of linear dependence" [35], which seemed in 1935. the most aim of the paper used to be to set up the basic (abstract) homes of the options of linear dependence and independence in vector areas, and to take advantage of those for the axiomatic definition of a brand new algebraic item, particularly the matroid. in addition, Whitney confirmed that those axioms also are abstractions of yes graph-theoretic techniques. this is often a great deal in proof whilst one considers the fundamental options making up the constitution of a matroid: a few mirror their linear algebraic foundation, whereas others mirror their graph-theoretic beginning. Whitney additionally studied a few vital examples of matroids. the subsequent significant improvement used to be caused within the forties through R. Rado's matroid generalisation of P. Hall's well-known "marriage" theorem. This supplied new impulses for transversal concept, during which matroids this present day play a vital position below the identify of "independence structures", cf. the treatise on transversal concept through L. Mirsky [26J. At approximately an analogous time R.P. Dilworth estab lished the relationship among matroids and lattice idea. hence matroids turned an important a part of combinatorial arithmetic. approximately ten years later W.T. Tutte [30] constructed the funda mentals of matroids intimately from a graph-theoretic perspective, and characterized image matroids in addition to the bigger type of these matroids which are representable over any field.