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arXiv · 1904.03562

Extension-lifting Bijections for Oriented Matroids

Spencer Backman·Francisco Santos·Chi Ho Yuen
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Abstract

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.

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Spencer Backman, Francisco Santos, Chi Ho Yuen. 2019-04-07. Extension-lifting Bijections for Oriented Matroids. https://doi.org/10.1007/s00454-026-00834-w

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