Relationship To Spreads
Translation planes are related to spreads in finite projective spaces by the André/Bruck-Bose construction. A spread of is a set of q2 + 1 lines, with no two intersecting. Equivalently, it is a partition of the points of into lines.
Given a spread of, the André/Bruck-Bose construction1 produces a translation plane of order q2 as follows: Embed as a hyperplane of . Define an incidence structure with "points," the points of not on and "lines" the planes of meeting in a line of . Then is a translation affine plane of order q2. Let be the projective completion of .
Read more about this topic: Translation Plane
Famous quotes containing the words relationship and/or spreads:
“There is a relationship between cartooning and people like Miró and Picasso which may not be understood by the cartoonist, but it definitely is related even in the early Disney.”
—Roy Lichtenstein (b. 1923)
“Dandyism is the last flicker of heroism in decadent ages.... Dandyism is a setting sun; like the declining star, it is magnificent, without heat and full of melancholy. But alas! the rising tide of democracy, which spreads everywhere and reduces everything to the same level, is daily carrying away these last champions of human pride, and submerging, in the waters of oblivion, the last traces of these remarkable myrmidons.”
—Charles Baudelaire (1821–1867)