{"paper":{"title":"Technical report Existence of Kirkman signal sets on $v=1,3\\pmod{6}$ points, $14\\leq v \\leq 3000$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Donald L. Kreher, Melissa S. Keranen","submitted_at":"2017-07-23T11:15:36Z","abstract_excerpt":"A partial Steiner triple system whose triples can be partitioned into $s$ partial parallel classes, each of size $m$, is a $signal$ $set$, denoted $\\mbox{SS}(v,s,m)$. A $Kirkman$ $signal$ $set$ $\\mbox{KSS}(v,m)$ is an $\\mbox{SS}(v,s,m)$ with $s=\\lfloor\\mu(v)/m\\rfloor$. When $v \\equiv 1$ or $3 \\pmod{6}$, then $\\mu(v)=b$, so the decomposition of an $\\mbox{STS}(v)$ into partial parallel classes of size $m$ is equivalent to a $\\mbox{KSS}(v,m)$. Table of known existence results is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.07282","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"}