Oriented Matroids

By Jürgen Richter-Gebert, Günter M. Ziegler. Handbook of Discrete and Computational Geometry, 2nd Ed., 2017

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Analysis of a greedy active learning strategy (2004, background): “Existing active learning schemes ignore the rich algebraic structure of Ĥ , an arrangement of hyperplanes [4].”
Perverse sheaves over real hyperplane arrangements (2014, background): “on ˝ was introduced by Tits [12] in 1974 in the context of buildings (which includes arrangements of root hyperplanes) and later, independently, by Bj¨orner, Las Vergnas, Sturmfels, White and Ziegler [3] for oriented matroids (which includes all hyperplane arrangements). For simplicity, we will refe”
Max-Min Representation of Piecewise Linear Functions (2000, background): “We consider H as a hyperplane arrangement [1] and denote T the family of nonempty intersections of the regions of H with int(Γ).”
Analytic Combinatorics in Several Variables (2013, background): “The combinatorics of the set CIRC can be axiomatized and many facts deduced; for a more complete discussion of matroids, see Björner et al. (1999). We let T denote the set { j ∈ A : LT ⊆ P j}; in other words, T is the maximal set of hyperplanes having intersection LT .”