{"paper":{"title":"The indecomposable tournaments $T$ with $\\mid W_{5}(T) \\mid = \\mid T \\mid -2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Houmem Belkhechine, Imed Boudabbous, Kaouthar Hzami","submitted_at":"2013-07-18T17:54:24Z","abstract_excerpt":"We consider a tournament $T=(V, A)$. For $X\\subseteq V$, the subtournament of $T$ induced by $X$ is $T[X] = (X, A \\cap (X \\times X))$. An interval of $T$ is a subset $X$ of $V$ such that for $a, b\\in X$ and $ x\\in V\\setminus X$, $(a,x)\\in A$ if and only if $(b,x)\\in A$. The trivial intervals of $T$ are $\\emptyset$, $\\{x\\}(x\\in V)$ and $V$. A tournament is indecomposable if all its intervals are trivial. For $n\\geq 2$, $W_{2n+1}$ denotes the unique indecomposable tournament defined on $\\{0,\\dots,2n\\}$ such that $W_{2n+1}[\\{0,\\dots,2n-1\\}]$ is the usual total order. Given an indecomposable tourn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5027","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"}