{"paper":{"title":"${\\rm{TS}}(v,\\lambda)$ with cyclic 2-intersecting Gray codes: $v\\equiv 0$ or $4\\pmod{12}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"John Asplund, Melissa Keranen","submitted_at":"2018-05-01T20:05:41Z","abstract_excerpt":"A ${\\rm{TS}}(v,\\lambda)$ is a pair $(V,\\mathcal{B})$ where $V$ contains $v$ points and $\\mathcal{B}$ contains $3$-element subsets of $V$ so that each pair in $V$ appears in exactly $\\lambda$ blocks. A $2$-block intersection graph ($2$-BIG) of a ${\\rm{TS}}(v,\\lambda)$ is a graph where each vertex is represented by a block from the ${\\rm{TS}}(v,\\lambda)$ and each pair of blocks $B_i,B_j\\in \\mathcal{B}$ are joined by an edge if $|B_i\\cap B_j|=2$. Using constructions for ${\\rm{TS}}(v,\\lambda)$ given by Schreiber, we show that there exists a ${\\rm{TS}}(v,\\lambda)$ for $v\\equiv 0$ or $4\\pmod{12}$ wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00535","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"}