The Axiomatization of Affine Oriented Matroids Reassessed
Andrea Baum, Yida Zhu
TL;DR
This paper revisits Johan Karlander's 1992 axiomatization of affine oriented matroids, identifies errors, and offers a corrected, simplified proof to strengthen the theoretical foundation of the subject.
Contribution
It provides a corrected and simplified proof of the axiomatization of affine oriented matroids, addressing previous inaccuracies in Karlander's work.
Findings
Identified errors in the original axiomatization
Provided a valid alternative proof
Enhanced understanding of affine oriented matroids
Abstract
In an unpublished manuscript of 1992, Johan Karlander has given an axiomatization of affine oriented matroids. 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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Taxonomy
TopicsAdvanced Algebra and Logic · Advanced Combinatorial Mathematics · Data Management and Algorithms