{"paper":{"title":"$d$-Degree Erd\\H{o}s-Ko-Rado theorem for finite vector spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Junling Zhou, Yunjing Shan","submitted_at":"2024-11-27T01:46:27Z","abstract_excerpt":"Let $V$ be an $n$-dimensional vector space over the finite field $\\mathbb{F}_{q}$ and let $\\left[V\\atop k\\right]_q$ denote the family of all $k$-dimensional subspaces of $V$. A family $\\mathcal{F}\\subseteq \\left[V\\atop k\\right]_q$ is called intersecting if for all $F$, $F'\\in\\mathcal{F}$, we have ${\\rm dim}$$(F\\cap F')\\geq 1$. Let $\\delta_{d}(\\mathcal{F})$ denote the minimum degree in $\\mathcal{F}$ of all $d$-dimensional subspaces. In this paper we show that $\\delta_{d}(\\mathcal{F})\\leq \\left[n-d-1\\atop k-d-1\\right]$ in any intersecting family $\\mathcal{F}\\subseteq \\left[V\\atop k\\right]_q$, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17985","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/2411.17985/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"}