Journal of Geometry

, 109:11 | Cite as

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In an unpublished manuscript of 1992, Johan Karlander has given an axiomatization of affine oriented matroids, which can be thought of as oriented matroids with a hyperplane at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.

Keywords

Oriented matroid sign vector arrangment of hyperplanes 

Mathematics Subject Classification

Primary 52C40 Secondary 52C35 

Notes

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.

References

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universität HamburgHamburgGermany
  2. 2.Universität TrierTrierGermany

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