{"paper":{"title":"On formal inverse of the Prouhet-Thue-Morse sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Maciej Gawro, Maciej Ulas","submitted_at":"2016-01-19T09:38:38Z","abstract_excerpt":"Let $p$ be a prime number and consider a $p$-automatic sequence ${\\bf u}=(u_{n})_{n\\in\\N}$ and its generating function $U(X)=\\sum_{n=0}^{\\infty}u_{n}X^{n}\\in\\mathbb{F}_{p}[[X]]$. Moreover, let us suppose that $u_{0}=0$ and $u_{1}\\neq 0$ and consider the formal power series $V\\in\\mathbb{F}_{p}[[X]]$ which is a compositional inverse of $U(X)$, i.e., $U(V(X))=V(U(X))=X$. In this note we initiate the study of arithmetic properties of the sequence of coefficients of the power series $V(X)$. We are mainly interested in the case when $u_{n}=t_{n}$, where $t_{n}=s_{2}(n)\\pmod{2}$ and ${\\bf t}=(t_{n})_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.04840","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"}