{"paper":{"title":"Isomorphy up to complementation","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hamza Si Kaddour, Maurice Pouzet","submitted_at":"2015-01-21T14:41:58Z","abstract_excerpt":"Considering uniform hypergraphs, we prove that for every non-negative integer $h$ there exist two non-negative integers $k$ and $t$ with $k\\leq t$ such that two $h$-uniform hypergraphs ${\\mathcal H}$ and ${\\mathcal H}'$ on the same set $V$ of vertices, with $| V| \\geq t$, are equal up to complementation whenever ${\\mathcal H}$ and ${\\mathcal H}'$ are $k$-{hypomorphic up to complementation}. Let $s(h)$ be the least integer $k$ such that the conclusion above holds and let $v(h)$ be the least $t$ corresponding to $k=s(h)$. We prove that $s(h)= h+2^{\\lfloor \\log_2 h\\rfloor} $. In the special case "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05181","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"}