Abstract
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<2 in the symplectic or unitary cases, and c<3 in the orthogonal case.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
