tools in its study. In a separate usage, a Fano plane is a projective plane that never satisfies Fano's axiom; in other words, the diagonal points of a...

of the Fano plane, a finite geometry in which the diagonal points of a complete quadrangle are collinear, some authors have augmented the axioms of projective...

structures. An alternative to adding the axiom is to refer to incidence structures that do not satisfy the axiom as being trivial and those that do as non-trivial...

authors give a treatment that embraces the Fano plane PG(2, 2) as the smallest finite projective plane. An axiom system that achieves this is as follows:...

Gino Fano (5 January 1871 – 8 November 1952) was an Italian mathematician, best known as the founder of finite geometry. He was born to a wealthy Jewish...

defined over a field that does not have even characteristic include Fano's axiom; The three diagonal points of a complete quadrangle are never collinear...

developed by the Italian mathematician Gino Fano. In his work on proving the independence of the set of axioms for projective n-space that he developed,...

not be these geometric objects. Some examples of incidence structures 1. Fano plane 2. Non-uniform structure 3. Generalized quadrangle 4. Möbius–Kantor...

b = b ⋅ a {\displaystyle \forall a,b\in D,\quad a\cdot b=b\cdot a} . Fano's axiom (which states a certain intersection does not happen) holds in P 2 D...

example of a matroid defined in this way is the Fano matroid, a rank three matroid derived from the Fano plane, a finite geometry with seven points (the...

the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These...

infinite, such as the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective...

infinite, such as the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective...

elements of G are called lines. L is a linear space if the following three axioms hold: (L1) two distinct points are incident with exactly one line. (L2)...

affine plane is a system of points and lines that satisfy the following axioms: Any two distinct points lie on a unique line. Given any line and any point...

cyclic group. Some groups can be proven to be isomorphic, relying on the axiom of choice, but the proof does not indicate how to construct a concrete isomorphism...

Not every matroid has a representation over every field, for instance, the Fano plane is representable only over fields of characteristic two. Other matroids...

{x} \cdot \mathbf {y} \right)=0,} if x × x = 0 is assumed as a separate axiom. Given the properties of bilinearity, orthogonality and magnitude, a nonzero...

projective space known as the Fano plane. Because of this connection, the Kelly–Moser example has also been called the non-Fano configuration. The other counterexample...

space. Gino Fano was an early writer in the area of Galois geometries. In his article of 1892, on proving the independence of his set of axioms for projective...

demonstrated two techniques to exclude such sets—the axiom of foundation and the notion of class. The axiom of foundation proposed that every set can be constructed...

open coloring axiom) consistent with 2 ℵ 0 > ℵ 2 {\displaystyle 2^{\aleph _{0}}>\aleph _{2}} ? Reinhardt cardinals: Without assuming the axiom of choice,...

tested with finite geometry. The simplest instance is PG(3,2), which has Fano planes as its 2-dimensional subspaces. It is an instance of Galois geometry...

is defined to be a family of subsets of a finite set, satisfying certain axioms. The sets in the family are called "independent sets". One of the ways of...

declassified 1949 – Robert M. Fano publishes Transmission of Information. M.I.T. Press, Cambridge, Massachusetts – Shannon–Fano coding 1949 – Leon G. Kraft...

it is covered by open affine subvarieties and satisfies the separation axiom. Thus, the local study of X (e.g., singularity) reduces to that of an affine...

technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. The latter problem...

points of the Fano plane (projective plane over F2); this can also be seen as the action on order 2 biplane, which is the complementary Fano plane. L2(11)...

U. Fano is also known for Feshbach–Fano partitioning, Fano factor, Fano noise, Lu–Fano plot, Fano effect, Fano–Lichten mechanism, Beutler-Fano profile...

each element a to an "orthocomplement" a⊥ in such a way that the following axioms are satisfied: Complement law a⊥ ∨ a = 1 and a⊥ ∧ a = 0. Involution law...