{"paper":{"title":"Cyclic, Simple and Indecomposable Three-fold Triple Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bradley Sheppard, Daniela Silvesan, Nabil Shalaby","submitted_at":"2014-04-02T12:14:27Z","abstract_excerpt":"In 2000, Rees and Shalaby constructed simple indecomposable two-fold cyclic triple systems for all v congruent to 0, 1, 3, 4, 7, and 9 (mod 12) where v = 4 or v>11, using Skolem-type sequences. We construct, using Skolem-type sequences, three-fold triple systems having the properties of being cyclic, simple, and indecomposable for all admissible orders v, with some possible exceptions for v = 9 and v = 24c + 57, where c >1 is a constant. To prove the simplicity we used a Mathematica computer program. We list in the Appendix the code and the results of the program."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0528","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"}