{"paper":{"title":"The {-3}-reconstruction and the {-3}-self duality of tournaments","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abderrahim Boussairi, Mouna Achour, Youssef Boudabbous","submitted_at":"2012-04-11T18:26:56Z","abstract_excerpt":"Let T = (V,A) be a (finite) tournament and k be a non negative integer. For every subset X of V is associated the subtournament T[X] = (X,A\\cap (X \\timesX)) of T, induced by X. The dual tournament of T, denoted by T\\ast, is the tournament obtained from T by reversing all its arcs. The tournament T is self dual if it is isomorphic to its dual. T is {-k}-self dual if for each set X of k vertices, T[V \\ X] is self dual. T is strongly self dual if each of its induced subtournaments is self dual. A subset I of V is an interval of T if for a, b \\in I and for x \\in V \\ I, (a,x) \\in A if and only if ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2513","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"}