{"paper":{"title":"Bounds for entries of $\\gamma$-vectors of flag homology spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Eran Nevo, Jean-Philippe Labb\\'e","submitted_at":"2016-12-04T19:07:36Z","abstract_excerpt":"We present some enumerative and structural results for flag homology spheres. For a flag homology sphere $\\Delta$, we show that its $\\gamma$-vector $\\gamma^\\Delta=(1,\\gamma_1,\\gamma_2,\\ldots)$ satisfies: \\begin{align*}\n  \\gamma_j=0,\\text{ for all } j>\\gamma_1, \\quad \\gamma_2\\leq\\binom{\\gamma_1}{2}, \\quad \\gamma_{\\gamma_1}\\in\\{0,1\\}, \\quad \\text{ and }\\gamma_{\\gamma_1-1}\\in\\{0,1,2,\\gamma_1\\}, \\end{align*} supporting a conjecture of Nevo and Petersen. Further we characterize the possible structures for $\\Delta$ in extremal cases. As an application, the techniques used produce infinitely many $f$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01169","kind":"arxiv","version":2},"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"}