Tropical hyperplane arrangements and oriented matroids
By Federico Ardila, M. Develin. 2007
73 citations recorded by the source corpus.
We study the combinatorial properties of a tropical hyperplane arrangement. We define tropical oriented matroids, and prove that they share many of the properties of ordinary oriented matroids. We show that a tropical oriented matroid determines a subdivision of a product of two simplices, and conjecture that this correspondence is a bijection.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/502690c13197914f5c8e6db96bffa353ff8b4e3b
How researchers see this paper
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In Computational Theory and Mathematics
- Lauren K. Williams
- David E. Speyer
- D. Nadler
- Eric Katz
- Alex Fink
- Jenia Tevelev
- Bernd Sturmfels
- Federico Ardila
In Discrete Mathematics and Combinatorics
- David E. Speyer
- Lauren K. Williams
- D. Nadler
- Thomas Lam
- Greg Muller
- Yuji Kodama
- Bernard Leclerc
- Federico Ardila
In Geometry and Topology
- Lauren K. Williams
- David E. Speyer
- D. Nadler
- Thomas Lam
- Eric Katz
- Yuji Kodama
- Greg Muller
- Bernard Leclerc
Citations in the corpus
- The positive Dressian equals the positive tropical Grassmannian (2020, background): “ical pseudohyperplane arrangements to subdivisions of the product of simplices. We now explain how to go between tropical pseudohyperplane arrangements and subdivisions of I. This section is based on [AD09], which initiated the study of tropical oriented matroids and conjectured that they are in bij”
- Arboreal Singularities (2013, background): “Pα̂ = iα̂!iα̂Pα u // Pα // iα!jα∗j αPα = Sα [1] //”