{"paper":{"title":"A stability result using the matrix norm to bound the permanent","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Pat Devlin, Ross Berkowitz","submitted_at":"2016-06-23T20:54:47Z","abstract_excerpt":"We prove a stability version of a general result that bounds the permanent of a matrix in terms of its operator norm. More specifically, suppose $A$ is an $n \\times n$ matrix over $\\mathbb{C}$ (resp. $\\mathbb{R}$), and let $\\mathcal{P}$ denote the set of $n \\times n$ matrices over $\\mathbb{C}$ (resp. $\\mathbb{R}$) that can be written as a permutation matrix times a unitary diagonal matrix. Then it is known that the permanent of $A$ satisfies $|\\text{perm}(A)| \\leq \\Vert A \\Vert_{2} ^n$ with equality iff $A/ \\Vert A \\Vert_{2} \\in \\mathcal{P}$ (where $\\Vert A \\Vert_2$ is the operator $2$-norm of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07474","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"}