Statements (41)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
gptkb:combinatorial_geometry
optimization linear programming discrete geometry oriented graphs topological representation theorem |
| gptkbp:definedIn |
circuits
axioms on sign vectors chirotopes covectors |
| gptkbp:field |
gptkb:combinatorics
gptkb:geometry gptkb:topology matroid theory |
| gptkbp:hasProperty |
studied since 1970s
abstracts hyperplane arrangements can be non-realizable captures orientation information finite set system generalizes matroids studied in algebraic combinatorics studied in computational geometry studied in discrete mathematics used in topological representation theorem |
| gptkbp:introduced |
gptkb:Michel_Las_Vergnas
gptkb:Günter_M._Ziegler gptkb:Bernd_Sturmfels gptkb:Anders_Björner gptkb:Neil_White |
| gptkbp:notableWork |
gptkb:Matroid_Theory_(book)
gptkb:Handbook_of_Combinatorics Oriented Matroids (book) |
| gptkbp:relatedTo |
convex polytopes
matroids hyperplane arrangements realizability sign vectors |
| gptkbp:bfsParent |
gptkb:Anders_Björner
|
| gptkbp:bfsLayer |
7
|
| https://www.w3.org/2000/01/rdf-schema#label |
Oriented Matroids
|