{"paper":{"title":"The probability of spanning a classical space by two non-degenerate subspaces of complementary dimension","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Alice C. Niemeyer, Cheryl E. Praeger, S.P. Glasby","submitted_at":"2021-09-21T08:06:27Z","abstract_excerpt":"Let $n,n'$ be positive integers and let $V$ be an $(n+n')$-dimensional vector space over a finite field $\\mathbb{F}$ 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 $1-c/|\\mathbb{F}|$ for some constant $c\\leqslant 2$ in the symplectic or unitary cases, and $c<3$ in the orthogonal case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.10015","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2109.10015/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}