{"paper":{"title":"The Formal Inverse of the Period-Doubling Sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL"],"primary_cat":"math.CO","authors_text":"Manon Stipulanti, Narad Rampersad","submitted_at":"2018-07-31T16:22:08Z","abstract_excerpt":"If $p$ is a prime number, consider a $p$-automatic sequence $(u_n)_{n\\ge 0}$, and let $U(X) = \\sum_{n\\ge 0} u_n X^n \\in \\mathbb{F}_p[[X]]$ be its generating function. Assume that there exists a formal power series $V(X) = \\sum_{n\\ge 0} v_n X^n \\in \\mathbb{F}_p[[X]]$ which is the compositional inverse of $U$, i.e., $U(V(X))=X=V(U(X))$. The problem investigated in this paper is to study the properties of the sequence $(v_n)_{n\\ge 0}$. The work was first initiated for the Thue-Morse sequence, and more recently the case of two variations of the Baum-Sweet sequence has been treated. In this paper, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11899","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"}