About: Incidence structure

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In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects. Consider the points and lines of the Euclidean plane as the two types of objects and ignore all the properties of this geometry except for the relation of which points are on which lines for all points and lines. What is left is the incidence structure of the Euclidean plane.

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rdfs:label	Inzidenzstruktur (de) Structure d'incidence (fr) Incidence structure (en) 결합 구조 (ko) Структура инцидентности (ru) Структура інцидентності (uk)
rdfs:comment	Inzidenzstruktur bezeichnet in der Mathematik, insbesondere der Geometrie, eine Struktur, die durch eine Menge von Punkten und eine dazu disjunkte Menge von Blöcken sowie eine zwischen diesen Mengen festgelegte Inzidenzrelation gegeben ist. Die Inzidenzrelation gibt aus der Menge aller möglichen Paare von Punkten und Blöcken nur jene an, die eine Inzidenz eines Punktes mit einem Block (z. B. einer Linie) bezeichnen. Durch die allgemein gehaltene Formulierung lassen sich zahlreiche Strukturen als Spezialfälle einer Inzidenzstruktur beschreiben. (de) 기하학에서 결합 구조(結合構造, 영어: incidence structure)는 두 집합 및 그 사이의 어떤 이항 관계로 구성된 수학적 구조이다. 일부 경우, 이는 각각 점과 직선으로 이루어진 기하계로 해석될 수 있다. (ko) In mathematics, an incidence structure is an abstract system consisting of two types of objects and a single relationship between these types of objects. Consider the points and lines of the Euclidean plane as the two types of objects and ignore all the properties of this geometry except for the relation of which points are on which lines for all points and lines. What is left is the incidence structure of the Euclidean plane. (en) En mathématiques, une structure d'incidence est toute composition de deux types d'objets dans le plan euclidien : des points ou l'équivalent de points et des droites ou l'équivalent de droites et d'une seule relation possible entre ces types, les autres propriétés étant ignorées et la structure pouvant ainsi se représenter par une matrice. Cette réduction de la complexité est à l'origine de l'émergence du concept dans d'autres domaines sous des formes propres. (fr) Структура инцидентности — в математике тройка где P — это множество «точек», L — множество «линий», а — отношение инцидентности. Элементы называются флагами. Если, мы говорим, что точка p «лежит на» линии . Можно представить L как множество подмножеств P, и инцидентностью I будет включение ( в том и только в том случае, когда ), но можно думать более абстрактно. (ru) У математиці структурою інцидентності називається трійка де P — це множина «точок», L — множина «ліній», а — відношення інцидентності. Елементи називаються прапорами. Якщо , ми кажемо, що точка p «лежить на» лінії . Можна уявити L як множину підмножин P, і інцидентністю I буде включення ( тоді і тільки тоді, коли ), але можна думати більш абстрактно. (uk)
foaf:depiction
dcterms:subject	Combinatorics Finite geometry Families of sets Incidence geometry
Wikipage page ID	723125 (xsd:integer)
Wikipage revision ID	1109180737 (xsd:integer)
Link from a Wikipage to another Wikipage	Prentice Hall Projective plane Element (mathematics) Partial linear space University of California, Riverside Incidence geometry Levi graph Complex plane Connected graph Mathematics Matrix (mathematics) Generalized quadrangle Symmetric matrix Eigenvector GF(2) Graph (discrete mathematics) Graph coloring Multipartite graph Converse relation Ergebnisse der Mathematik und ihrer Grenzgebiete Ordered geometry Pappus configuration Automorphism Heawood graph Linear space (geometry) Linear subspace Square matrix Affine plane (incidence geometry) Combinatorics Duality (projective geometry) Finite geometry Nim addition Family of sets Fano plane Graph theory Marcel Dekker Isomorphic Hypergraph Abstract polytope Families of sets Incidence geometry Affine plane Binary number Bipartite graph Block design H.S.M. Coxeter Incidence (geometry) Loop (graph theory) Universal set Euclidean plane Finite geometry Möbius plane Möbius–Kantor configuration Heterogeneous relation Multiple edges Transpose matrix Springer-Verlag Simple graph Set system John Baez Symmetry (mathematics) Projective configuration

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