In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects...

In mathematics, incidence geometry is the study of incidence structures. A geometric structure such as the Euclidean plane is a complicated object that...

Incidence list, a concept in graph theory Incidence matrix, a matrix that shows the relationship between two classes of objects Incidence structure,...

mathematics, an incidence matrix is a logical matrix that shows the relationship between two classes of objects, usually called an incidence relation. If...

graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points and lines in an incidence geometry or...

parallel class structure of an affine plane of order n may be used to construct a set of n − 1 mutually orthogonal latin squares. Only the incidence relations...

Hopcroft's problem of finding point–line incidences Incidence matrix Incidence algebra Incidence structure Incidence geometry Levi graph Hilbert's axioms...

polyhedra Incidence structures generalize planes (such as affine, projective, and Möbius planes) as can be seen from their axiomatic definitions. Incidence structures...

by playing on an arbitrary incidence structure, where rows are lines and cells are points. Tic-tac-toe's incidence structure consists of nine points, three...

universal set. Hypergraphs can be viewed as incidence structures. In particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every...

In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as blocks, chosen such...

projective geometry, an intersection theorem or incidence theorem is a statement concerning an incidence structure – consisting of points, lines, and possibly...

simplicial complex. An incidence structure consists of a set of points, a set of lines, and an (arbitrary) binary relation, called the incidence relation, specifying...

that facts are independent of any metric structure. Under the projective transformations, the incidence structure and the relation of projective harmonic...

alpha subunit, a class of proteins Generalized quadrangle, a type of incidence structure in mathematics Generalized quantifier, a type of expression in linguistic...

Euclidean reflection. More generally, a Möbius plane is an incidence structure with the same incidence relationships as the classical Möbius plane. It is one...

combinatorial structures now known as abstract polytopes was first described by Egon Schulte in his 1980 PhD dissertation. In it he defined "regular incidence complexes"...

finite incidence structure, so many of its properties can be established using combinatorial techniques and other tools used in the study of incidence geometries...

but with some additional restrictions: every two points of the incidence structure can be associated with at most one line, and every two lines can...

shared by all projective planes. A projective plane is a rank 2 incidence structure ( P , L , I ) {\displaystyle ({\mathcal {P}},{\mathcal {L}},I)} consisting...

arrangement of polygons that can be folded up to form a polyhedron An incidence structure consisting of points and parallel classes of lines An operator algebra...

elements lies in just one block. These incidence structures have been generalized with block designs. The incidence matrix used in these geometrical contexts...

maximal flag has exactly r elements. An incidence geometry of rank 2 is commonly called an incidence structure with elements of type 1 called points and...

Grazing incidence diffraction (GID) is a technique for interrogating a material using small incidence angles for an incoming wave, often leading to the...

space defined axiomatically in terms of an incidence structure (a set of points P, lines L, and an incidence relation I specifying which points lie on...

In geometry, a generalized quadrangle is an incidence structure whose main feature is the lack of any triangles yet containing many quadrangles. A generalized...

In mathematics, a generalized polygon is an incidence structure introduced by Jacques Tits in 1959. Generalized n-gons encompass as special cases projective...

(1974, 10.13), is a Tits building of type F4 (a specific generalized incidence structure). The four types of vertices are called points, lines, planes, and...

In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set and commutative...

counting points, lines, and planes on the diagonal. The incidences are expressed off diagonal. The structure is self dual, swapping points and planes, expressed...