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Engstr\\\"om proved that the independence polynomial satisfies $|I(G;-1)| \\leq 2^{\\phi(G)}$ for any graph $G$, and this bound is best possible. Levit and Mandrescu provided an elementary proof of the bound, and in addition conjectured that for every positive integer $k$ and integer $q$ with $|q|\\leq 2^k$, th"},"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":"1410.7726","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-10-28T18:38:23Z","cross_cats_sorted":[],"title_canon_sha256":"3c34d92d0cdbe13c0ebf5f2c7d09257cead7a383d4a95f5124ccb28b0a7ce7b3","abstract_canon_sha256":"5d287ad90ebe0176326aa580047509652855922fda2902c0091ada9afd65d65f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:09.614429Z","signature_b64":"G3vg2C+wVuS3tR1L2dcAJkFQHVJblR1V6GntkUFDcNgc43vmY/LRJ8wcVwaUgFSW0vp6ZBbguzrdfQVWSWn+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f225eda954a04c7149fd55ae7ff87f816b7add3c0afb55930cc504cd93e451f2","last_reissued_at":"2026-05-18T02:39:09.613888Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:09.613888Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the values of independence polynomials at $-1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jonathan Cutler, Nathan Kahl","submitted_at":"2014-10-28T18:38:23Z","abstract_excerpt":"The independence polynomial $I(G;x)$ of a graph $G$ is $I(G;x)=\\sum_{k=1}^{\\alpha(G)} s_k x^k$, where $s_k$ is the number of independent sets in $G$ of size $k$. 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