Extension-lifting Bijections for Oriented Matroids

Extending the notion of geometric bijections for regular matroids, introduced by the first and third author with Matthew Baker, we describe a family of bijections between bases of an oriented matroid and special orientations. These bijections are specified by a pair of circuit and cocircuit signatur...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Backman, Spencer, Santos, Francisco, Chi Ho Yuen
Format: Article
Language:English
Subjects:
Polynomials
Signatures
Online Access:Get full text
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Summary:Extending the notion of geometric bijections for regular matroids, introduced by the first and third author with Matthew Baker, we describe a family of bijections between bases of an oriented matroid and special orientations. These bijections are specified by a pair of circuit and cocircuit signatures coming respectively from a generic single-element lifting and extension. We then characterize generic single-element liftings and extensions using these bijections. We also explain the relation of our work with the works of Gioan--Las Vergnas and Ding. Some implications in oriented matroid programming and oriented matroid triangulations are also discussed.
ISSN:2331-8422