Extension-Lifting Bijections for Oriented Matroids
Abstract
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 reorientations of it. 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 works of Gioan–Las Vergnas and Ding. Some implications in oriented matroid programming and oriented matroid triangulations are also discussed.
Fields of Study & Subjects
Advanced Graph Theory Research
Logic
programming
and type systems
Formal Methods in Verification
Publication details
- Journal / source
- Discrete & Computational Geometry
- Publisher
- Springer Science and Business Media LLC
- Volume
- 75
- Issue
- 3
- Pages
- 969–994
- Publication date
- 18 March 2026
- Language
- EN