{"paper":{"title":"Block-avoiding point sequencings of directed triple systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donald L. Kreher, Douglas R. Stinson, Shannon Veitch","submitted_at":"2019-07-25T16:46:48Z","abstract_excerpt":"A directed triple system of order $v$ (or, DTS$(v)$) is decomposition of the complete directed graph $\\vec{K_v}$ into transitive triples. A $v$-good sequencing of a DTS$(v)$ is a permutation of the points of the design, say $[x_1 \\; \\cdots \\; x_v]$, such that, for every triple $(x,y,z)$ in the design, it is not the case that $x = x_i$, $y = x_j$ and $z = x_k$ with $i < j < k$. We prove that there exists a DTS$(v)$ having a $v$-good sequencing for all positive integers $v \\equiv 0,1 \\bmod {3}$. Further, for all positive integers $v \\equiv 0,1 \\bmod {3}$, $v \\geq 7$, we prove that there is a DTS"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11186","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"}