Projective geometries of congruence and finite projective geometries

Pauli graph and finite projective lines/geometries

The commutation relations between the generalized Pauli operators of N -qudits (i. e., N p-level quantum systems), and the structure of their maximal sets of commuting bases, follow a nice graph theoretical/geometrical pattern. One may identify vertices/points with the operators so that edges/lines join commuting pairs of them to form the so-called Pauli graph PpN . As per two-qubits (p = 2, N ...

Finite Projective Plane Geometries and Difference Sets

Fuzzy projective geometries

In and we introduced a rst model of fuzzy projective geometries deduced from respectively fuzzy vector spaces and fuzzy groups This provided a link between the fuzzy versions of classical theories that are very closely related However the geometric structure involved in this model is rather weak a fuzzy projec tive space in this sense is equivalent with a given se quence of subspaces in the bas...

Codegree problems for projective geometries

The codegree density γ(F ) of an r-graph F is the largest number γ such that there are F -free r-graphs G on n vertices such that every set of r−1 vertices is contained in at least (γ−o(1))n edges. When F = PG2(2) is the Fano plane Mubayi showed that γ(F ) = 1/2. This paper studies γ(PGm(q)) for further values of m and q. In particular we have an upper bound γ(PGm(q)) ≤ 1− 1/m for any projectiv...

Projective geometries in dense matroids

We prove that, given integers l, q ≥ 2 and n there exists an integer α such that, if M is a simple matroid with no l + 2point line minor and at least αq elements, then M contains a PG(n− 1, q′)-minor, for some prime-power q′ > q.