{"paper":{"title":"The Young Tableaux Hopf algebra and multiple Schur series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.QA"],"primary_cat":"math.NT","authors_text":"Jinbo Yu","submitted_at":"2026-07-10T07:23:36Z","abstract_excerpt":"In this paper, we introduce multiple Schur series, which are defined by Schur-type sums over semi-standard Young tableaux and generalize both Schur multiple zeta values and multiple Eisenstein series. To study their algebraic structure, we construct a connected, commutative, graded Hopf algebra of Young tableaux and identify its linearized quotient with the quasi-shuffle algebra. Within this Hopf algebra and its quotient, we establish several relations, including a hook formula and the Jacobi--Trudi formula. Furthermore, we relate this Hopf algebra to the ring of symmetric functions, which yie"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09157","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.09157/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}