{"paper":{"title":"Random generation of direct sums of finite non-degenerate subspaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alice C. Niemeyer, Cheryl E. Praeger, S. P. Glasby","submitted_at":"2021-11-03T13:06:47Z","abstract_excerpt":"Let $V$ be a $d$-dimensional vector space over a finite field $\\mathbb{F}$ equipped with a non-degenerate hermitian, alternating, or quadratic form. Suppose $|\\mathbb{F}|=q^2$ if $V$ is hermitian, and $|\\mathbb{F}|=q$ otherwise. Given integers $e, e'$ such that $e+e'\\leqslant d$, we estimate the proportion of pairs $(U, U')$, where $U$ is a non-degenerate $e$-subspace of $V$ and $U'$ is a non-degenerate $e'$-subspace of $V$, such that $U\\cap U'=0$ and $U\\oplus U'$ is non-degenerate (the sum $U\\oplus U'$ is direct and usually not perpendicular). The proportion is shown to be positive and at lea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.02198","kind":"arxiv","version":2},"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/2111.02198/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"}