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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.02937","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-02-09T18:46:54Z","cross_cats_sorted":["cs.DM","cs.IT","math.CO","math.IT","math.PR"],"title_canon_sha256":"2908e2d963d5c512a8a1a2bf0516cf7b7a32e2684476dcdcac54d7a74584ebd5","abstract_canon_sha256":"54e1009aca2170c0b2bc8ebbca45fe17fe51046a063cc5f9fabb9a1943b9e2d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:02.005401Z","signature_b64":"4Lc9eoZ5BpckyhF6XtTPyTm+rY2BZ57Fg4kwXpYLERPvHt5zx6aQSRM6x/ZZlAKep1cdNr0DyfmXzkwIv1J4Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94b468f22f1cbde71a6d321be495804f2da56a9390678451cd6cc89cb825a6e9","last_reissued_at":"2026-05-18T00:51:02.004815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:02.004815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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