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In this paper, we observe the behaviors of roots of SSNN polynomials which are a wider class of the polynomials containing all the Ehrhart polynomials of Gorenstein Fano polytopes. As a result, we verify that this conjecture is true when the roots are real numbers or when $d \\leq 5$."},"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":"1112.5777","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-12-25T11:55:45Z","cross_cats_sorted":[],"title_canon_sha256":"8be713e9148684fe2d83079300bfc2f3cca51a15fdd17bed57d22a43ed3aa578","abstract_canon_sha256":"3b86c1409a460855ae49f473911e00145c573f0d33cf29950c2fb319f900c2e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:40:49.526890Z","signature_b64":"5cwlW+EeFHE7fPNyA+8I8b2wj/g5gm+aQwu+n0szyELe+rhWJRHzA9SCaAyKQA8VHgGk/Gc3PY+kT1sSCFzeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5241585fffc37666c73613b784c5702b91e4a8a920e01fc2bef7adcfd2a586e3","last_reissued_at":"2026-05-18T03:40:49.525971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:40:49.525971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Roots of Ehrhart polynomials and symmetric $\\delta$-vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Akihiro Higashitani","submitted_at":"2011-12-25T11:55:45Z","abstract_excerpt":"The conjecture on roots of Ehrhart polynomials, stated by Matsui et al. \\cite[Conjecture 4.10]{MHNOH}, says that all roots $\\alpha$ of the Ehrhart polynomial of a Gorenstein Fano polytope of dimension $d$ satisfy $-\\frac{d}{2} \\leq \\Re(\\alpha) \\leq \\frac{d}{2} -1$. In this paper, we observe the behaviors of roots of SSNN polynomials which are a wider class of the polynomials containing all the Ehrhart polynomials of Gorenstein Fano polytopes. 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