{"paper":{"title":"Transforming Recurrent Sequences by Using the Binomial and Invert Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nadir Murru, Stefano Barbero, Umberto Cerruti","submitted_at":"2011-05-11T09:59:29Z","abstract_excerpt":"In this paper we study the action of the Binomial and Invert (interpolated) operators on the set of linear recurrent sequences. We prove that these operators preserve this set, and we determine how they change the characteristic polynomials. We show that these operators, with the aid of two other elementary operators (essentially the left and right shifts), can transform any impulse sequence (a linear recurrent sequence starting from $(0,...,0,1)$) into any other impulse sequence, by two processes that we call \\emph{construction} and \\emph{deconstruction}. Finally, we give some applications to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2143","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"}