{"paper":{"title":"Classical Sturmian sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Alexei Zhedanov","submitted_at":"2019-04-08T01:05:29Z","abstract_excerpt":"The Sturm sequence is generated by a pair of polynomials $P(x)$ and $P'(x)$, where $P(x)$ is assumed to have simple real roots. Euclidean algorithm generates then a finite sequence of polynomials orthogonal on the grid $x_s$ of roots of the polynomial $P(x)$. This algorithm can be exploited in order to find the number of roots of the polynomial $P(x)$ inside a given interval. We consider the \"inverse\" problem: what is the explicit system of orthogonal polynomials generated by the prescribed grid $x_s$ of \"classical\" type. The main results are the following. The generic linear grid generates a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03789","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"}