{"paper":{"title":"On the regularity of the Hankel determinant sequence of the characteristic sequence of powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.NT","authors_text":"Ying-jun Guo","submitted_at":"2018-06-20T12:59:55Z","abstract_excerpt":"For any sequences $\\mathbf{u}=\\{u(n)\\}_{n\\geq0}, \\mathbf{v}=\\{v(n)\\}_{n\\geq0},$ we define $\\mathbf{u}\\mathbf{v}:=\\{u(n)v(n)\\}_{n\\geq0}$ and $\\mathbf{u}+\\mathbf{v}:=\\{u(n)+v(n)\\}_{n\\geq0}$. Let $f_i(x)~(0\\leq i< k)$ be sequence polynomials whose coefficients are integer sequences. We say an integer sequence $\\mathbf{u}=\\{u(n)\\}_{n\\geq0}$ is a polynomial generated sequence if $$\\{u(kn+i)\\}_{n\\geq0}=f_i(\\mathbf{u}),~(0\\leq i< k).$$ %Here we define $\\mathbf{u}\\mathbf{v}:=\\{u(n)v(n)\\}_{n\\geq0}$ and $\\mathbf{u}+\\mathbf{v}:=\\{u(n)+v(n)\\}_{n\\geq0}$ for any two sequences $\\mathbf{u}=\\{u(n)\\}_{n\\geq0}, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.08729","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"}