{"paper":{"title":"On two non-existence results for Cameron-Liebler $k$-sets in $\\mathrm{PG}(n,q)$","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jan De Beule, Jonathan Mannaert, Leo Storme","submitted_at":"2024-03-01T13:30:29Z","abstract_excerpt":"This paper focuses on non-existence results for Cameron-Liebler $k$-sets. A Cameron-Liebler $k$-set is a collection of $k$-spaces in $\\mathrm{PG}(n,q)$ or $\\mathrm{AG}(n,q)$ admitting a certain parameter $x$, which is dependent on the size of this collection. One of the main research questions remains the (non-)existence of Cameron-Liebler $k$-sets with parameter $x$. This paper improves two non-existence results. First we show that the parameter of a non-trivial Cameron-Liebler $k$-set in $\\mathrm{PG}(n,q)$ should be larger than $q^{n-\\frac{5k}{2}-1}$, which is an improvement of an earlier kn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.00519","kind":"arxiv","version":1},"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/2403.00519/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"}