{"paper":{"title":"A Common Generalization to Theorems on Set Systems with $\\mathcal{L}$-intersections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jimeng Xiao, Jiuqiang Liu, Shenggui Zhang","submitted_at":"2017-07-06T10:15:55Z","abstract_excerpt":"In this paper, we provide a common generalization to the well-known Erd\\H{o}s-Ko-Rado Theorem, Frankl-Wilson Theorem, Alon-Babai-Suzuki Theorem, and Snevily Theorem on set systems with $\\mathcal{L}$-intersections. As a consequence, we derive a result which strengthens substantially the well-known theorem on set systems with $k$-wise $\\mathcal{L}$-intersections by F$\\ddot{u}$redi and Sudakov [J. Combin. Theory, Ser. A (2004) 105: 143-159]. We will also derive similar results on $\\mathcal{L}$-intersecting families of subspaces of an $n$-dimensional vector space over a finite field $\\mathbb{F}_{q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01715","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":""},"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"}