{"paper":{"title":"(Pure) transcendence bases in $\\phi$-deformed shuffle bialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CO","math.GR","math.MP"],"primary_cat":"cs.SC","authors_text":"Christophe Tollu (LIPN), G\\'erard H.E. Duchamp (LIPN), Quoc Hoan Ng\\^o (LIPN), Van Chi\\^en Bui (LIPN), Vincel Hoang Ngoc Minh (LIPN)","submitted_at":"2015-07-04T09:25:07Z","abstract_excerpt":"Computations with integro-differential operators are often carried out in an associative algebra with unit, and they are essentially non-commutative computations. By adjoining a cocommutative co-product, one can have those operators perform act on a bialgebra isomorphic to an enveloping algebra. That gives an adequate framework for a computer-algebra implementation via monoidal factorization, (pure) transcendence bases and Poincar\\'e--Birkhoff--Witt bases. In this paper, we systematically study these deformations, obtaining necessary and sufficient conditions for the operators to exist, and we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01089","kind":"arxiv","version":2},"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"}