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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.5027","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-18T17:54:24Z","cross_cats_sorted":[],"title_canon_sha256":"c39bfcdec81cafa68553e8259eee58821c423057b2e80da5dd8ba4ec45a5e071","abstract_canon_sha256":"44e485766ed2406f9219ccf43c8c475ce0c7ba6e55dfc48d576ac6d401f6b397"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:06.894881Z","signature_b64":"3umhZ3by7GFbJVW1gK5MlZIXQJKQNTNqeDd5pNorR/u8+q2E8aAvS1wHsI+hyT3W5l+FsHXxMNzfha3FazD6DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7869118a9ad27aa6c9fdfb70d5f5b5b2a1e38424a58d19eef8ca4e2e05d56e4c","last_reissued_at":"2026-05-18T03:18:06.894180Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:06.894180Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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