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The axiomatization of affine oriented matroids reassessed

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Abstract

In an unpublished manuscript of 1992, Johan Karlander has given an axiomatization of affine oriented matroids, which can be thought of as oriented matroids with a hyperplane at infinity. A closer examination of the text revealed an invalid construction and an incorrect argument in the proof of his main theorem. This paper provides an alternative argument to fix and slightly simplify the proof of the main theorem.

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Acknowledgements

The authors are particularly grateful to Hans-Jürgen Bandelt and Nathan Bowler (Hamburg) for their valuable suggestions and comments that greatly improved the manuscript and motivated the last section. Moreover, author Yida Zhu is partly supported by the German Research Foundation (DFG) within the research training group 2126 Algorithmic Optimization.

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Authors and Affiliations

  1. Universität Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    Andrea Baum

  2. Universität Trier, Universitätsring 15, 54295, Trier, Germany

    Yida Zhu

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  1. Andrea Baum
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  2. Yida Zhu
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Correspondence to Yida Zhu.

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Baum, A., Zhu, Y. The axiomatization of affine oriented matroids reassessed. J. Geom. 109, 11 (2018). https://doi.org/10.1007/s00022-018-0407-5

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  • DOI: https://doi.org/10.1007/s00022-018-0407-5

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