• Corpus ID: 237581499

The probability of spanning a classical space by two non-degenerate subspaces of complementary dimension

  title={The probability of spanning a classical space by two non-degenerate subspaces of complementary dimension},
  author={Stephen P. Glasby and Alice C. Niemeyer and Cheryl E. Praeger},
Let n, n be positive integers and let V be an (n+n)-dimensional vector space over a finite field F equipped with a non-degenerate alternating, hermitian or quadratic form. We estimate the proportion of pairs (U, U ), where U is a non-degenerate n-subspace and U ′ is a non-degenerate n-subspace of V , such that U +U ′ = V (usually such spaces U and U ′ are not perpendicular). The proportion is shown to be at least 1 − c/|F| for some constant c 6 2 in the symplectic or unitary cases, and c < 3 in… 

Tables from this paper


Lattices generated by two orbits of subspaces under finite classical groups
By ordering L by ordinary or reverse inclusion, two families of atomic lattices are obtained and the subspaces in these lattices is characterized and classifies their geometricity.
Intersection theorems for systems of finite vector spaces
  • W. Hsieh
  • Mathematics, Computer Science
    Discret. Math.
  • 1975
Application of Erdos, Ko and Rado methods to the analogous subset problem leads to improvement on the Erdos-Ko-Rado bounds.
Orthogonal graphs over finite commutative rings of odd characteristic
The graph is vertex and arc transitive and the chromatic number is determined and the graph is an orthogonal graph, which is a strongly regular or quasi-strongly regular graph and its automorphism group is obtained.
Cyclic Matrices Over Finite Fields
Adxd matrix X over a field F is said to be cyclic if its characteristic polynomial cx{t) is equal to its minimal polynomial mx(t). This condition guarantees that the vector space V:= F of 1 x d row
On the dual code of points and generators on the Hermitian variety H(2n+1, q2)
The minimum distance problem for general n is solved, the n smallest types of code words are classified and the small weight code words as being a linear combination of these n types are characterized.
Constructive recognition of classical groups in even characteristic
Abstract Let G = 〈 X 〉 ⩽ GL ( d , F ) be a classical group in its natural representation defined over a finite field F of even characteristic. We present Las Vegas algorithms to construct standard
The Angle Between Complementary Subspaces
Usually the discussion stops right there, and extensions to angles between subspaces of higher dimensions are, more or less tacitly, shoved under the rug. Perhaps this is because most instructors
The Subgroup Structure of the Finite Classical Groups
1. Motivation and setting for the results 2. Basic properties of the classical groups 3. The statement of the main theorem 4. The structure and conjugacy of the members of C 5. Properties of the
Generation of finite classical groups by pairs of elements with large fixed point spaces
We study `good elements' in finite $2n$-dimensional classical groups $G$: namely $t$ is a `good element' if $o(t)$ is divisible by a primitive prime divisor of $q^n-1$ for the relevant field order
A Hilton-Milner Theorem for Vector Spaces
It is shown that if any intersecting family of $k$-subspaces of an $n$-dimensional vector space over $GF(q)$ with $\bigcap_{F \in {\cal F}} F=0$ has size at mostq, then the chromatic number of the corresponding $q$-Kneser graphs is determined.