Fano plane [SEP] named after
Fano plane
In finite geometry, the Fano plane (after Gino Fano) is the finite projective plane of order 2. It is the finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point. The standard notation for this plane, as a member of a family of projective spaces, is where stands for "projective geometry", the first parameter is the geometric dimension and the second parameter is the order.
only for the projective spaces over GF(2), of which the Fano plane is an example.
In a Sylvester matroid, every independent set can be augmented by one more element to form a circuit of the matroid.
Sylvester matroids cannot be represented over the real numbers (this is the Sylvester–Gallai theorem), nor can they be oriented.
History.
Sylvester matroids were studied and named by after James Joseph Sylvester, because they violate the Sylvester–Gallai theorem (for points and lines in the