{"paper":{"title":"New Facets of the QAP-Polytope","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Pawan Kumar Aurora, Shashank K Mehta","submitted_at":"2014-09-02T11:18:53Z","abstract_excerpt":"The Birkhoff polytope is defined to be the convex hull of permutation matrices, $P_{\\sigma}\\ \\forall \\sigma\\in S_n$. We define a second-order permutation matrix $P^{[2]}_{\\sigma}$ in $\\mathbb{R}^{n^2\\times n^2}$ corresponding to a permutation $\\sigma$ as $(P^{[2]}_{\\sigma})_{ij,kl} = (P_{\\sigma})_{ij}(P_{\\sigma})_{kl}$. We call the convex hull of the second-order permutation matrices, the {\\em second-order Birkhoff polytope} and denote it by ${\\cal B}^{[2]}$. It can be seen that ${\\cal B}^{[2]}$ is isomorphic to the QAP-polytope, the domain of optimization in {\\em quadratic assignment problem}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0667","kind":"arxiv","version":2},"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"}