WebAug 5, 2015 · We study computational aspects of the General Position Subset Selection problem defined as follows: Given a set of points in the plane, find a maximum-cardinality subset of points in general... WebJan 13, 2024 · There are theorems on general position in more complicated situations (for example, Bertini theorems, and the Lefschetz theorem on a hyperplane section); in …
Strong notions of general position - MathOverflow
General position is a property of configurations of points, or more generally other subvarieties (lines in general position, so no three concurrent, and the like). General position is an extrinsic notion, which depends on an embedding as a subvariety. Informally, subvarieties are in general position if they cannot be … See more In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general case situation, as opposed to some more special or … See more Different geometries allow different notions of geometric constraints. For example, a circle is a concept that makes sense in See more In intersection theory, both in algebraic geometry and in geometric topology, the analogous notion of transversality is used: subvarieties in general intersect transversally, … See more A set of points in a d-dimensional affine space (d-dimensional Euclidean space is a common example) is in general linear position (or just general position) if no k of them lie in a (k − 2)- See more This definition can be generalized further: one may speak of points in general position with respect to a fixed class of algebraic relations (e.g. conic sections). In algebraic geometry this kind of condition is frequently encountered, in that points should impose … See more In very abstract terms, general position is a discussion of generic properties of a configuration space; in this context one means properties that hold on the generic point of a configuration space, or equivalently on a Zariski-open set. This notion … See more WebJun 6, 2024 · For example, for a rational linear representation of a semi-simple group $ G $ in a vector space $ V $, the orbits of the points in general position are closed if and only if their stabilizers are reductive (see ); when $ G $ is irreducible, an explicit expression of the stabilizers of the points in general position has been found (see , ). The ... creative development in children
Is there a general geometric characterization for polynomials to be …
WebApr 19, 2024 · It is a well-known result due to Boros and Füredi [] that for every set P of n points in the plane in general position there exists a point of depth at least \({2}\left( {\begin{array}{c}n\\ 3\end{array}}\right) /9\), where the depth of a point x is the number of triangles spanned by P that contain x in their interior.For an alternative proof of this fact … WebIn computational geometry, finite sets of points with no three in line are said to be in general position. In this terminology, the no-three-in-line problem seeks the largest subset of a grid that is in general position, but researchers have also considered the problem of finding the largest general position subset of other non-grid sets of points. WebMar 29, 2016 · If then is one point. If then is a projective line. If then is a projective hyperplane. The following definition is necessary to define a projective basis. Definition: A set of points in is in general position if for all , every subset of points in is not contained in a projective subspace of dimension . creative diagnostics download