{"paper":{"title":"A Generalization of Permanent Inequalities and Applications in Counting and Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.IT","math.CO","math.IT","math.PR"],"primary_cat":"cs.DS","authors_text":"Nima Anari, Shayan Oveis Gharan","submitted_at":"2017-02-09T18:46:54Z","abstract_excerpt":"A polynomial $p\\in\\mathbb{R}[z_1,\\dots,z_n]$ is real stable if it has no roots in the upper-half complex plane. Gurvits's permanent inequality gives a lower bound on the coefficient of the $z_1z_2\\dots z_n$ monomial of a real stable polynomial $p$ with nonnegative coefficients. This fundamental inequality has been used to attack several counting and optimization problems.\n  Here, we study a more general question: Given a stable multilinear polynomial $p$ with nonnegative coefficients and a set of monomials $S$, we show that if the polynomial obtained by summing up all monomials in $S$ is real "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02937","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"}