{"paper":{"title":"Enumerative $g$-theorems for the Veronese construction for formal power series and graded algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Martina Kubitzke, Volkmar Welker","submitted_at":"2011-08-14T09:13:23Z","abstract_excerpt":"Let $(a_n)_{n \\geq 0}$ be a sequence of integers such that its generating series satisfies $\\sum_{n \\geq 0} a_nt^n = \\frac{h(t)}{(1-t)^d}$ for some polynomial $h(t)$. For any $r \\geq 1$ we study the coefficient sequence of the numerator polynomial $h_0(a^{<r >}) +...+ h_{\\lambda'}(a^{<r >}) t^{\\lambda'}$ of the $r$\\textsuperscript{th} Veronese series $a^{<r >}(t) = \\sum_{n \\geq 0} a_{nr} t^n$. Under mild hypothesis we show that the vector of successive differences of this sequence up to the $\\lfloor \\frac{d}{2} \\rfloor$\\textsuperscript{th} entry is the $f$-vector of a simplicial complex for la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2852","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"}