{"paper":{"title":"Intersecting faces of a simplicial complex via algebraic shifting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"S. A. Seyed Fakhari","submitted_at":"2012-02-22T15:41:50Z","abstract_excerpt":"A family $\\mathcal{A}$ of sets is {\\it $t$-intersecting} if the cardinality of the intersection of every pair of sets in $\\mathcal{A}$ is at least $t$, and is an {\\it $r$-family} if every set in $\\mathcal{A}$ has cardinality $r$. A well-known theorem of Erd\\H{o}s, Ko, and Rado bounds the cardinality of a $t$-intersecting $r$-family of subsets of an $n$-element set, or equivalently of $(r-1)$-dimensional faces of a simplex with $n$ vertices. As a generalization of the Erd\\H{o}s-Ko-Rado theorem, Borg presented a conjecture concerning the size of a $t$-intersecting $r$-family of faces of an arbit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4942","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":""},"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"}