منابع مشابه
Space versus Time: Unimodular versus Non-Unimodular Projective Ring Geometries?
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to be unleashed for physics. There exist specific rings over which the projective spaces feature two principally distinct kinds of basic constituents (points and...
متن کاملFuzzy 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...
متن کاملCodegree 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...
متن کاملProjective 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.
متن کاملThe Turán problem for projective geometries
We consider the following Turán problem. How many edges can there be in a (q + 1)-uniform hypergraph on n vertices that does not contain a copy of the projective geometry PGm(q)? The case q = m = 2 (the Fano plane) was recently solved independently and simultaneously by Keevash and Sudakov (The Turán number of the Fano plane, Combinatorica, to appear) and Füredi and Simonovits (Triple systems n...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1985
ISSN: 0021-8693
DOI: 10.1016/0021-8693(85)90105-x