{"paper":{"title":"More nonexistence results for symmetric pair coverings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Horsley, Nevena Franceti\\'c, Sarada Herke","submitted_at":"2015-05-22T04:51:59Z","abstract_excerpt":"A $(v,k,\\lambda)$-covering is a pair $(V, \\mathcal{B})$, where $V$ is a $v$-set of points and $\\mathcal{B}$ is a collection of $k$-subsets of $V$ (called blocks), such that every unordered pair of points in $V$ is contained in at least $\\lambda$ blocks in $\\mathcal{B}$. The excess of such a covering is the multigraph on vertex set $V$ in which the edge between vertices $x$ and $y$ has multiplicity $r_{xy}-\\lambda$, where $r_{xy}$ is the number of blocks which contain the pair $\\{x,y\\}$. A covering is symmetric if it has the same number of blocks as points. Bryant et al.(2011) adapted the deter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.05949","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"}