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330.105 --- Wiskundige economie. Wiskundige methoden in de economie --- 330.105 Wiskundige economie. Wiskundige methoden in de economie

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Mathematics --- 330.105 --- Economics, Mathematical --- Economics --- Mathematical economics --- Econometrics --- Wiskundige economie. Wiskundige methoden in de economie --- Methodology --- 330.105 Wiskundige economie. Wiskundige methoden in de economie

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Mathematics --- Economics, Mathematical --- 330.105 --- Economics --- Mathematical economics --- Econometrics --- Wiskundige economie. Wiskundige methoden in de economie --- Methodology --- 330.105 Wiskundige economie. Wiskundige methoden in de economie

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Matroid theory has its origin in a paper by H. Whitney entitled "On the abstract properties of linear dependence" [35], which appeared in 1935. The main objective of the paper was to establish the essential (abstract) properties of the concepts of linear dependence and independence in vector spaces, and to use these for the axiomatic definition of a new algebraic object, namely the matroid. Furthermore, Whitney showed that these axioms are also abstractions of certain graph-theoretic concepts. This is very much in evidence when one considers the basic concepts making up the structure of a matroid: some reflect their linear­ algebraic origin, while others reflect their graph-theoretic origin. Whitney also studied a number of important examples of matroids. The next major development was brought about in the forties by R. Rado's matroid generalisation of P. Hall's famous "marriage" theorem. This provided new impulses for transversal theory, in which matroids today play an essential role under the name of "independence structures", cf. the treatise on transversal theory by L. Mirsky [26J. At roughly the same time R.P. Dilworth estab­ lished the connection between matroids and lattice theory. Thus matroids became an essential part of combinatorial mathematics. About ten years later W.T. Tutte [30] developed the funda­ mentals of matroids in detail from a graph-theoretic point of view, and characterised graphic matroids as well as the larger class of those matroids that are representable over any field.

Discrete mathematics --- Matroids --- Business & Economics --- Economic Theory --- 330.105 --- Wiskundige economie. Wiskundige methoden in de economie --- 330.105 Wiskundige economie. Wiskundige methoden in de economie

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This volume on the proceedings of a symposium on Resource Allocation and Division of Space represents a revised interest in the old problem of allocation and a fresh attack on the increasingly vital problem of space management. The symposium was held at the Toba International Hotel, near Nagoya, Japan in December, 1975. Although the contributions included in this volume are all broadly concerned with either resource allocation or spatial problems, the editors have selected papers essentially on the basis of scientific merits and orginality rather than on the basis of narrowly focused topics and titles. The result is that all of the papers included, ranging from growth, index number, space density function, factor mobility, concentration and accumulation between sectors and spaces, distributions, relationship between spatial structure and organizational structure to the application of Lie group to production functions, are of the highest quality. It is the intention and belief of the editors that this collection of wide ranging but highly original papers is a major contribution to the advancement of economic science. The editors feel that a symposium of this kind is worthwhile and should be held at regular intervals. The list of contributions can be divided into two parts. Part I, consisting of papers 1 through 9, deals in general with allocation. Papers 10 through 13 compose Part II, which is primarily concerned with spatial problems.

Distribution strategy --- Economic geography --- 330.105 --- Wiskundige economie. Wiskundige methoden in de economie --- Business & Economics --- Economic Theory --- 330.105 Wiskundige economie. Wiskundige methoden in de economie