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

S. P. Glasby, Alice C. Niemeyer, Cheryl E. Praeger

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Article number102055
JournalFinite Fields and Their Applications
Volume82
DOIs
Publication statusPublished - Sep 2022

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