{"paper":{"title":"Inversion of some series of free quasi-symmetric functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Florent Hivert, Jean-Christophe Novelli, Jean-Yves Thibon","submitted_at":"2008-09-25T19:35:08Z","abstract_excerpt":"We give a combinatorial formula for the inverses of the alternating sums of free quasi-symmetric functions of the form F_{\\omega(I)} where I runs over compositions with parts in a prescribed set C. This proves in particular three special cases (no restriction, even parts, and all parts equal to 2) which were conjectured by B. C. V. Ung in [Proc. FPSAC'98, Toronto]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4480","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"}