{"paper":{"title":"On exponentials of exponential generating series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.NT","authors_text":"Roland Bacher (IF)","submitted_at":"2008-07-03T11:51:25Z","abstract_excerpt":"Identifying the algebra of exponential generating series with the shuffle algebra of formal power series, one can define an exponential map ${\\mathop{exp}}_!:X\\mathbb K[[X]]\\longrightarrow 1+X\\mathbb K[[X]]$ for the associated Lie group formed by exponential generating series with constant coefficient 1 over an arbitrary field $\\mathbb K$. The main result of this paper states that the map ${\\mathop{exp}}_!$ (and its inverse map ${\\mathop{log}}_!$) induces a bijection between rational, respectively algebraic, series in $X\\mathbb K [[X]]$ and $1+X\\mathbb K[[X]]$ if the field $\\mathbb K$ is a sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0540","kind":"arxiv","version":4},"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"}