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 ℓ.
An incidence structure has no concept of a point being in between two other points, the order of points on a line is undefined.
the dual structure
is obtained, where I* is the inverse relation of I. Clearly
Each hypergraph or set system can be regarded as an incidence structure in which the universal set plays the role of "points", the corresponding family of sets plays the role of "lines" and the incidence relation is set membership "∈". Conversely, every incidence structure can be viewed as a hypergraph.
In particular, let
The corresponding incidence structure is called the Fano plane.
Each incidence structure corresponds to a bipartite graph called Levi graph or incidence graph with a given black and white vertex coloring where black vertices correspond to points and white vertices correspond to lines of and the edges correspond to flags.
US Patent Issued to Sony on July 17 for "Information Processing Device and Information Processing Method, Image Processing Device and Image Processing Method, and Computer Program" (Japanese Inventor)
Jul 21, 2012; ALEXANDRIA, Va., July 21 -- United States Patent no. 8,224,089, issued on July 17, was assigned to Sony Corp. (Tokyo)....