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mathematics (31) 31
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Discrete and Computational Geometry, ISSN 0179-5376, 03/2016, Volume 55, Issue 2, pp. 284 - 295
Consider arrangements of n pseudolines in the real projective plane. Let denote the number of intersection points where exactly k pseudolines are incident. We... 
(Formula presented.) inequalities for arrangements of lines | Partitions of projective plane | Pseudoline arrangement | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | t(k) inequalities for arrangements of lines | Lower bounds | Positioning | Computational geometry | Construction | Planes | Inequalities | Texts | Combinatorial analysis
Journal Article
Periodica Mathematica Hungarica, ISSN 0031-5303, 12/2018, Volume 77, Issue 2, pp. 164 - 174
We study a non-trivial extreme case of the orchard problem for 12 pseudolines and we provide a complete classification of pseudoline arrangements having 19... 
Orchard problem | Pseudoline arrangements | Sylvester’s problem | Line arrangements | MATHEMATICS | MATHEMATICS, APPLIED | Sylvester's problem | POWERS | Combinatorial analysis | Straight lines
Journal Article
Topology and its Applications, ISSN 0166-8641, 09/2015, Volume 193, pp. 226 - 247
It is clear that a geometric symmetry of a line arrangement induces a combinatorial one; we study the converse situation. We introduce a strategy that exploits... 
Rybnikov | Falk–Sturmfels | Oriented matroid | Matroid | Pseudoline arrangement | Falk-Sturmfels | MATHEMATICS | MATHEMATICS, APPLIED | PROJECTIVE LINES | MODULI SPACES
Journal Article
Advances in Applied Mathematics, ISSN 0196-8858, 04/2018, Volume 95, pp. 199 - 270
We initiate the study of group actions on (possibly infinite) semimatroids and geometric semilattices. To every such action is naturally associated an... 
Hyperplane arrangements | Posets | Tutte polynomials | Matroids | Pseudoline arrangements | Toric arrangements | Group actions | MATHEMATICS, APPLIED | ARRANGEMENTS | Algebra
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 3/2016, Volume 55, Issue 2, pp. 284 - 295
Consider arrangements of n pseudolines in the real projective plane. Let $$t_k$$ t k denote the number of intersection points where exactly k pseudolines are... 
Partitions of projective plane | Computational Mathematics and Numerical Analysis | Mathematics | Combinatorics | t_k$$ t k inequalities for arrangements of lines | Pseudoline arrangement
Journal Article
ARS MATHEMATICA CONTEMPORANEA, ISSN 1855-3966, 2018, Volume 14, Issue 1, pp. 97 - 116
It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not even admit... 
sweep | MATHEMATICS, APPLIED | allowable sequence of permutations | quasiline arrangement | incidence structure | wiring diagram | topological configuration | Pseudoline arrangement | maps on surfaces | MATHEMATICS | projective plane | geometric configuration | combinatorial configuration
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 10/2012, Volume 48, Issue 3, pp. 682 - 701
We compute all isomorphism classes of simplicial arrangements in the real projective plane with up to 27 lines. It turns out that Grünbaum’s catalogue is... 
Wiring | Computational Mathematics and Numerical Analysis | Arrangement of hyperplanes | Pseudoline | Mathematics | Simplicial | Combinatorics | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | WEYL GROUPOIDS | Geometry | Theorems | Computational geometry | Positioning | Planes | Classification | Byproducts | Isomorphism | Catalogues
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 10/2011, Volume 46, Issue 3, pp. 405 - 416
Arrangements of lines and pseudolines are important and appealing objects for research in discrete and computational geometry. We show that there are at most... 
Computational Mathematics and Numerical Analysis | Enumeration | Pseudoline | Cutpath | Mathematics | Combinatorial geometry | Combinatorics | MATHEMATICS | LINEAR ORDERS | ACYCLIC SETS | COMPUTER SCIENCE, THEORY & METHODS | BRUHAT ORDERS | Geometry | Computational mathematics | Computational geometry | Positioning | Planes | Coding | Upper bounds | Ingredients | Counting
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 10/2007, Volume 38, Issue 3, pp. 595 - 603
It is shown that if a simple Euclidean arrangement of n pseudolines has no (≥ 5)-gons, then it has exactly n - 2 triangles and (n - 2)(n - 3)/2 quadrilaterals.... 
Local Sequence | Computational Mathematics and Numerical Analysis | Internal Vertex | Inductive Hypothesis | Mathematics | Discrete Comput Geom | Combinatorics | Intersection Point | MATHEMATICS | TRIANGLES | NUMBER | COMPUTER SCIENCE, THEORY & METHODS | PSEUDOLINES | REAL PROJECTIVE PLANE | Geometry | Polyhedra
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 3/2011, Volume 45, Issue 2, pp. 279 - 302
Journal Article
Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 10/2019, Volume 167, pp. 213 - 256
We study the combinatorics of pseudoline arrangements and their relation to the geometry of flag and Schubert varieties. We associate to each pseudoline... 
Superpotential | String cone | Mirror Symmetry | Flag variety | Schubert variety | Combinatorics | Pseudoline arrangement | MATHEMATICS | CANONICAL BASES | TORIC DEGENERATIONS | CLUSTER ALGEBRAS | GEOMETRY
Journal Article
Computational Geometry: Theory and Applications, ISSN 0925-7721, 05/2015, Volume 48, Issue 4, pp. 295 - 310
A is a graph drawn in the plane so that any pair of edges have at most one point in common, which is either an endpoint or a proper crossing. is called if no... 
Saturated topological graph | Simple topological graph | Pseudoline arrangement | Simple topological graph Saturated topological graph Pseudoline arrangement | MATHEMATICS | MATHEMATICS, APPLIED | DISJOINT EDGES | Computer science | Computational geometry | Graphs | Construction | Graph theory | Topology | Planes | Mathematics - Combinatorics
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2001, Volume 109, Issue 1, pp. 67 - 94
Sweeping is an important algorithmic tool in geometry. In the first part of this paper we define sweeps of arrangements and use the "Sweeping Lemma" to show... 
Higher Bruhat order | Sweep | Pseudoline | Arrangement | 51G05 | 52C99 | 68U05 | 06A06 | arrangement | pseudoline | sweep | MATHEMATICS, APPLIED | HIGHER BRUHAT ORDERS | higher Bruhat order
Journal Article
Discrete Mathematics, ISSN 0012-365X, 2002, Volume 257, Issue 2, pp. 267 - 283
Given a set of n points in general position in the plane, where n is even, a halving line is a line going through two of the points and cutting the remaining... 
FINITE-SET | SEMISPACES | MATHEMATICS | NUMBER | PSEUDOLINES | PLANAR K-SETS
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 2006, Volume 154, Issue 17, pp. 2470 - 2483
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 03/2017, Volume 84, Issue 3, pp. 297 - 310
A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The pseudolinear... 
crossing number | rectilinear crossing number | pseudoline arrangements | pseudolinear crossing number | MATHEMATICS | Mathematics - Combinatorics
Journal Article
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 1998, Volume 1517, pp. 137 - 148
The number of triangles in arrangements of lines and pseudolines has been object of some research. Most results, however, concern arrangements in the... 
Euclidean plane | Triangle | Pseudoline | Arrangement | Strechability | arrangement | pseudoline | NUMBER | PSEUDOLINES | COMPUTER SCIENCE, THEORY & METHODS | triangle | strechability
Conference Proceeding
Discrete & Computational Geometry, ISSN 0179-5376, 10/1999, Volume 22, Issue 3, pp. 429 - 438
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 10/2013, Volume 50, Issue 3, pp. 552 - 648
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 7/2012, Volume 48, Issue 1, pp. 142 - 191
We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements... 
Computational Mathematics and Numerical Analysis | Enumeration algorithm | Sorting network | Pseudotriangulation | Multitriangulation | Mathematics | Combinatorics | Flip | Pseudoline arrangement | PSEUDO-TRIANGULATIONS | CONVEX POLYGON | COMPLEXES | MATHEMATICS | POLYTOPE | PLANE | COMPUTER SCIENCE, THEORY & METHODS | Employee motivation | Algorithms | Geometry | Mathematical models
Journal Article
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