Partial Geometries
One can construct partial geometries, derived from maximal arcs:
- Let K be a maximal arc with degree d. Consider the incidence structure, where P contains all points of the projective plane not on K, B contains all line of the projective plane intersecting K in d points, and the incidence I is the natural inclusion. This is a partial geometry : .
- Consider the space and let K a maximal arc of degree in a two-dimensional subspace . Consider an incidence structure where P contains all the points not in, B contains all lines not in and intersecting in a point in K, and I is again the natural inclusion. is again a partial geometry : .
Read more about this topic: Maximal Arc
Famous quotes containing the word partial:
“The only coöperation which is commonly possible is exceedingly partial and superficial; and what little true coöperation there is, is as if it were not, being a harmony inaudible to men. If a man has faith, he will coöperate with equal faith everywhere; if he has not faith, he will continue to live like the rest of the world, whatever company he is joined to.”
—Henry David Thoreau (1817–1862)