{"paper":{"title":"Infinitely many cyclic solutions to the Hamilton-Waterloo problem with odd length cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Francesca Merola, Tommaso Traetta","submitted_at":"2015-01-28T06:25:45Z","abstract_excerpt":"It is conjectured that for every pair $(\\ell,m)$ of odd integers greater than 2 with $m \\equiv 1\\; \\pmod{\\ell}$, there exists a cyclic two-factorization of $K_{\\ell m}$ having exactly $(m-1)/2$ factors of type $\\ell^m$ and all the others of type $m^{\\ell}$. The authors prove the conjecture in the affirmative when $\\ell \\equiv 1\\; \\pmod{4}$ and $m \\geq \\ell^2 -\\ell + 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06999","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"}