Corpus ID: 237581499

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

@inproceedings{Glasby2021ThePO,
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},
year={2021}
}
• Published 21 September 2021
• Mathematics
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… Expand

#### References

SHOWING 1-10 OF 24 REFERENCES
Lattices generated by two orbits of subspaces under finite classical groups
• Computer Science, Mathematics
• Finite Fields Their Appl.
• 2009
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. Expand
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. Expand
Orthogonal graphs over finite commutative rings of odd characteristic
• Computer Science, Mathematics
• Finite Fields Their Appl.
• 2016
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. Expand
Cyclic Matrices Over Finite Fields
• Mathematics
• 1995
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 rowExpand
On the dual code of points and generators on the Hermitian variety H(2n+1, q2)
• Mathematics, Computer Science
• 2014
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. Expand
Constructive recognition of classical groups in even characteristic
• Mathematics
• 2009
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 standardExpand
The Angle Between Complementary Subspaces
• Mathematics
• 1995
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 instructorsExpand
The Subgroup Structure of the Finite Classical Groups
• Mathematics
• 1990
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 theExpand
Generation of finite classical groups by pairs of elements with large fixed point spaces
• Mathematics
• 2014
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 orderExpand
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. Expand