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Apr 12, 2024 · Fano plane. In finite geometry, the Fano plane (after Gino Fano) is a 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. These points and lines cannot exist with this pattern of incidences in Euclidean geometry, but they can be given ...
The Fano plane. This particular projective plane is sometimes called the Fano plane. If any of the lines is removed from the plane, along with the points on that line, the resulting geometry is the affine plane of order 2. The Fano plane is called the projective plane of order 2 because it is unique (up to
Apr 20, 2018 · Turán's Theorem for the Fano plane. Louis Bellmann, Christian Reiher. Confirming a conjecture of Vera T. Sós in a very strong sense, we give a complete solution to Turán's hypergraph problem for the Fano plane. That is we prove for n\ge 8 that among all 3 -uniform hypergraphs on n vertices not containing the Fano plane there is indeed ...
The Fano plane cannot be represented in the Euclidean plane using only points and straight line segments (i.e., it is not realizable). This is a consequence of the Sylvester–Gallai theorem , according to which every realizable incidence geometry must include an ordinary line , a line containing only two points.
In finite geometry, the Fano plane (after Gino Fano) is a 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. These points and lines cannot exist with this pattern of incidences in Euclidean geometry, but they can be given coordinates ...
This can also apply to certain finite subsets of a plane, for example the fano plane, this consists only 7 points and 7 lines. Although each line contains 3 points it takes only 2 points to define the line also although each line is crossed by 3 lines it only takes 2 lines to define the point. We can see that one of the lines is a circle rather ...
subgroup G of the automorphism group of a graph C acts half-arc-transitively on. if the natural actions of G on the vertex-set and edge-set of C are both transitive, but the natural action of G on the arc-set of C is not transitive. When G 1⁄4 AutðCÞ the graph C is said to be half-arc-transitive. Given a bipartite cubic graph with a certain ...
