2N noncollinear points determine at least 2N directions

From MaRDI portal
Publication:1170240

DOI10.1016/0097-3165(82)90045-0zbMath0496.05001OpenAlexW1998563847MaRDI QIDQ1170240

Peter Ungar

Publication date: 1982

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0097-3165(82)90045-0




Related Items

Few slopes without collinearityOn the number of directions determined by a three-dimensional points setCrystal pop-stack sorting and type \(A\) crystal latticesPop-stack-sorting for Coxeter groupsStack-sorting for Coxeter groupsAreas of triangles and Beck's theorem in planes over finite fieldsGraph drawings with few slopesCoxeter pop-tsack torsingThe structure of sets with few sums along a graphExpanders with superquadratic growthA note on the minimum number of edge-directions of a convex polytopeLogarithmic bundles and line arrangements, an approach via the standard constructionA solution to a problem of Grünbaum and Motzkin and of Erdős and Purdy about bichromatic configurations of points in the planeOn the Minkowski distances and products of sum setsOn the growth rate in SL2(Fp)${\rm SL_2}(\mathbb {F}_p)$, the affine group and sum‐product type implicationsA family of four-variable expanders with quadratic growthPromotion sortingUngarian Markov chainsThe image of the pop operator on various latticesKaufman and Falconer estimates for radial projections and a continuum version of Beck's theoremA farewell to Ricky PollackOn sets of \(n\) points in general position that determine lines that can be pierced by \(n\) pointsOn the dimension and smoothness of radial projectionsUnnamed ItemUnnamed ItemOrdering points by linear functionalsUnnamed ItemThe complexity of point configurationsFertility monotonicity and average complexity of the stack-sorting mapAllowable interval sequences and separating convex sets in the planeOn Cartesian products which determine few distinct distancesSuballowable sequences and geometric permutationsHomotheties and incidencesUnnamed ItemOn supersolvable and nearly supersolvable line arrangementsStack-sorting with consecutive-pattern-avoiding stacksOn the geometry of real or complex supersolvable line arrangementsOn the Use of the Klein Quadric for Geometric Incidence Problems in Two DimensionsNew expander bounds from affine group energyA geometric condition for a hyperplane arrangement to be freeCounting \(k\)-projections of a point setDirection treesMeeting covered elements in \(\nu\)-Tamari latticesVariations on the Sum-Product ProblemOn the number of directions determined by the common tangents to a family of pairwise disjoint convex sets in the planeSemispaces of configurations, cell complexes of arrangementsNew sum-product estimates for real and complex numbersValid orderings of real hyperplane arrangements



Cites Work