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We analyze the independence polynomia"},"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":"1802.06298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-17T21:30:06Z","cross_cats_sorted":[],"title_canon_sha256":"95da9917ed53995436fe4ba7bae332242ef0baeaf871ec5252eae07fe97b85af","abstract_canon_sha256":"789decfb8a5755264b209ffe4069a45d887dfbcb6ca06b38fd5c29bc65dba158"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:03.755117Z","signature_b64":"Qx05g60uRZ1b2Q9euhrov9z1uHztaTnEZWK36TzbWebJhyVKt5Itqi8h3KxuNhu8hPn1gg5iPGemhdRG9kJoBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c59fe6515f6748e16168750683553ebf0438582d3abf6612e221da168e95faf","last_reissued_at":"2026-05-18T00:23:03.754571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:03.754571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unimodality of the independence polynomials of non-regular caterpillars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bailey Ethridge, Levente Szabo, Patrick Bahls","submitted_at":"2018-02-17T21:30:06Z","abstract_excerpt":"The independence polynomial $I(G, x)$ of a graph $G$ is the polynomial in variable $x$ in which the coefficient $a_n$ on $x^n$ gives the number of independent subsets $S \\subseteq V(G)$ of vertices of $G$ such that $|S| = n$. $I(G, x)$ is unimodal if there is an index $\\mu$ such that that $a_0 \\leq a_1 \\leq$...$\\leq a_{\\mu-1} \\leq a_{\\mu} \\geq a_{\\mu +1} \\geq$...$\\geq a_{d-1} \\geq a_d$ While the independence polynomials of many families of graphs with highly regular structure are known to be unimodal, little is known about less regularly structured graphs. 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