In mathematics, an incidence structure is a triple
where P is a set of "points", L is a set of "lines" and is the incidence relation. The elements of I are called flags. If
we say that point p "lies on" line . One may concretely have L be a set of subsets of P, and have incidence I be containment ( if and only if ), but one may also work more abstractly.
Incidence structures generalize planes (such as affine, projective, and Möbius planes) in their axiomatic definitions, as the terminology indicates. The higher-dimensional analog is called an incidence geometry.
Read more about Incidence Structure: Comparison With Other Structures, Dual Structure, Correspondence With Hypergraphs, Geometric Representation, Levi Graph of An Incidence Structure
Famous quotes containing the words incidence and/or structure:
“Hermann Goering, Joachim von Ribbentrop, Albert Speer, Walther Frank, Julius Streicher and Robert Ley did pass under my inspection and interrogation in 1945 but they only proved that National Socialism was a gangster interlude at a rather low order of mental capacity and with a surprisingly high incidence of alcoholism.”
—John Kenneth Galbraith (b. 1908)
“In the extent and proper structure of the Union, therefore, we behold a republican remedy for the diseases most incident to republican government.”
—James Madison (1751–1836)