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Transforms, Diagrams and Representations

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Contributions to Geometry

Abstract

A number of the more striking advances in the combinatorial theory of convexity in recent years have come from the various kinds of diagram techniques. With benefit of hindsight, we can trace the origins of the theory to Whitney [1935], a paper which also initiated the fruitful study of matroids (see also 8A below). However, the idea as presently envisaged first appears in a recognizable form in Gale [1956], though related ideas appear in Motzkin [1951] and Davis [1954]. The present development of the subject is due largely to Perles (whose work is described in Grünbaum [1967]) and, later, to a series of papers by McMullen and Shephard (references will be given later, in the appropriate places).

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Authors and Affiliations

  1. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, Britain

    P. McMullen

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  1. University of Siegen, Siegen, Deutschland

    Jürgen Tölke  & Jörg M. Wills  & 

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McMullen, P. (1979). Transforms, Diagrams and Representations. In: Tölke, J., Wills, J.M. (eds) Contributions to Geometry. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5765-9_4

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  • DOI: https://doi.org/10.1007/978-3-0348-5765-9_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-1048-6

  • Online ISBN: 978-3-0348-5765-9

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