{"paper":{"title":"On multiple and infinite log-concavity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Armin Straub, Luis A. Medina","submitted_at":"2014-05-07T22:03:52Z","abstract_excerpt":"Following Boros--Moll, a sequence $(a_n)$ is $m$-log-concave if $\\mathcal{L}^j (a_n) \\geq 0$ for all $j = 0, 1, \\ldots, m$. Here, $\\mathcal{L}$ is the operator defined by $\\mathcal{L} (a_n) = a_n^2 - a_{n - 1} a_{n + 1}$. By a criterion of Craven--Csordas and McNamara--Sagan it is known that a sequence is $\\infty$-log-concave if it satisfies the stronger inequality $a_k^2 \\geq r a_{k - 1} a_{k + 1}$ for large enough $r$. On the other hand, a recent result of Br\\\"and\\'en shows that $\\infty$-log-concave sequences include sequences whose generating polynomial has only negative real roots. In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1765","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"}