{"paper":{"title":"The enriched $q$-monomial basis of the quasisymmetric functions","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Darij Grinberg, Ekaterina A. Vassilieva","submitted_at":"2023-09-03T08:35:21Z","abstract_excerpt":"We construct a new family $\\left( \\eta_{\\alpha}^{\\left( q\\right) }\\right) _{\\alpha\\in\\operatorname*{Comp}}$ of quasisymmetric functions for each element $q$ of the base ring. We call them the \"enriched $q$-monomial quasisymmetric functions\". When $r:=q+1$ is invertible, this family is a basis of $\\operatorname{QSym}$. It generalizes Hoffman's \"essential quasi-symmetric functions\" (obtained for $q=0$) and Hsiao's \"monomial peak functions\" (obtained for $q=1$), but also includes the monomial quasisymmetric functions as a limiting case.\n  We describe these functions $\\eta_{\\alpha}^{\\left( q\\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.01118","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.01118/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"}