{"paper":{"title":"On the maximum number of spanning copies of an orientation in a tournament","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Raphael Yuster","submitted_at":"2015-11-24T16:20:27Z","abstract_excerpt":"For an orientation $H$ with $n$ vertices, let $T(H)$ denote the maximum possible number of labeled copies of $H$ in an $n$-vertex tournament. It is easily seen that $T(H) \\ge n!/2^{e(H)}$ as the latter is the expected number of such copies in a random tournament. For $n$ odd, let $R(H)$ denote the maximum possible number of labeled copies of $H$ in an $n$-vertex regular tournament. Adler et al. proved that, in fact, for $H=C_n$ the directed Hamilton cycle, $T(C_n) \\ge (e-o(1))n!/2^{n}$ and it was observed by Alon that already $R(C_n) \\ge (e-o(1))n!/2^{n}$. Similar results hold for the directed"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07784","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"}