Open access
Date
2022-12Type
- Journal Article
Abstract
In a previous work, we gave a construction of (not necessarily realisable) oriented matroids from a triangulation of a product of two simplices. In this follow-up paper, we use a combinatorial analogue of Viro's patchworking to derive a topological representation of the oriented matroid directly from the polyhedral structure of the triangulation. This provides a combinatorial manifestation of patchworking besides tropical algebraic geometry. We achieve this by defining a general homeomorphism-preserving operation on regular cell complexes which acts by merging adjacent cells in the complex together. We then rephrase the patchworking procedure in terms of this process using the theory of tropical oriented matroids. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000563946Publication status
publishedExternal links
Journal / series
Journal of the London Mathematical SocietyVolume
Pages / Article No.
Publisher
WileyMore
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