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

(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

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

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

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

Partitions of projective plane | Computational Mathematics and Numerical Analysis | Mathematics | Combinatorics | t_k$$ t k inequalities for arrangements of lines | Pseudoline arrangement

Journal Article

6.
Full Text
Combinatorial configurations, quasiline arrangements, and systems of curves on surfaces

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

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

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

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

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

We describe an incremental algorithm to enumerate the isomorphism classes of double pseudoline arrangements. The correction of our algorithm is based on the...

Arrangements of pseudolines | Mutations | Computational Mathematics and Numerical Analysis | Two-dimensional projective geometries | One-extension spaces | Enumeration algorithms | Mathematics | Chirotopes | Combinatorial geometry | Convexity | Combinatorics | Arrangements of double pseudolines | ORIENTED MATROIDS | MATHEMATICS | GENERATION | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Geometry | Isomorphism | Computational geometry | Positioning | Counting

Arrangements of pseudolines | Mutations | Computational Mathematics and Numerical Analysis | Two-dimensional projective geometries | One-extension spaces | Enumeration algorithms | Mathematics | Chirotopes | Combinatorial geometry | Convexity | Combinatorics | Arrangements of double pseudolines | ORIENTED MATROIDS | MATHEMATICS | GENERATION | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Geometry | Isomorphism | Computational geometry | Positioning | Counting

Journal Article

11.
Full Text
String cone and superpotential combinatorics for flag and Schubert varieties in type A

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

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

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

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

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

We study connectivity, Hamilton path and Hamilton cycle decomposition, 4-edge and 3-vertex coloring for geometric graphs arising from pseudoline (affine or...

Coloring | Circle and pseudocircle arrangement | Hamilton decomposition | Planar graph | Projective-planar graph | Hamilton path | Hamilton cycle | Connectivity | Line and pseudoline arrangement | MATHEMATICS, APPLIED | projective-planar graph | line and pseudoline arrangement | PLANAR GRAPHS | PATHS | planar graph | circle and pseudocircle arrangement | coloring connectivity

Coloring | Circle and pseudocircle arrangement | Hamilton decomposition | Planar graph | Projective-planar graph | Hamilton path | Hamilton cycle | Connectivity | Line and pseudoline arrangement | MATHEMATICS, APPLIED | projective-planar graph | line and pseudoline arrangement | PLANAR GRAPHS | PATHS | planar graph | circle and pseudocircle arrangement | coloring connectivity

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

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

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

The number of triangles in arrangements of lines and pseudolines has been the object of some research. Most results, however, concern arrangements in the...

Nontrivial Arrangement | Projective Plane | Simple Arrangement | Computational Mathematics and Numerical Analysis | Euclidean Plane | Mathematics | Combinatorics | Interesting Change | MATHEMATICS | NUMBER | COMPUTER SCIENCE, THEORY & METHODS | PSEUDOLINES | REAL PROJECTIVE PLANE | LINES | Positioning | Computational geometry | Euclidean geometry | Planes | Triangles | Aircraft detection | Proving

Nontrivial Arrangement | Projective Plane | Simple Arrangement | Computational Mathematics and Numerical Analysis | Euclidean Plane | Mathematics | Combinatorics | Interesting Change | MATHEMATICS | NUMBER | COMPUTER SCIENCE, THEORY & METHODS | PSEUDOLINES | REAL PROJECTIVE PLANE | LINES | Positioning | Computational geometry | Euclidean geometry | Planes | Triangles | Aircraft detection | Proving

Journal Article

Discrete & Computational Geometry, ISSN 0179-5376, 10/2013, Volume 50, Issue 3, pp. 552 - 648

We extend the classical LR characterization of chirotopes of finite planar families of points to chirotopes of finite planar families of pairwise disjoint...

Discrete geometry | Computational Mathematics and Numerical Analysis | Projective planes | Pseudoline arrangements | Mathematics | Chirotopes | Convexity | Combinatorics | ORIENTED MATROIDS | THEOREM | SPACES | PROOF | TOPOLOGICAL REPRESENTATION | CONJECTURE | MATHEMATICS | SETS | RANK 3 | COMPUTER SCIENCE, THEORY & METHODS | ARRANGEMENTS | Workshops (Educational programs) | Chemical properties | Geometry | Theorems | Constrictions | Tools | Computational geometry | Polarity | Mathematical analysis

Discrete geometry | Computational Mathematics and Numerical Analysis | Projective planes | Pseudoline arrangements | Mathematics | Chirotopes | Convexity | Combinatorics | ORIENTED MATROIDS | THEOREM | SPACES | PROOF | TOPOLOGICAL REPRESENTATION | CONJECTURE | MATHEMATICS | SETS | RANK 3 | COMPUTER SCIENCE, THEORY & METHODS | ARRANGEMENTS | Workshops (Educational programs) | Chemical properties | Geometry | Theorems | Constrictions | Tools | Computational geometry | Polarity | Mathematical analysis

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

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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