{"paper":{"title":"Hybrid Grothendieck polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.RT"],"primary_cat":"math.CO","authors_text":"Jiaji Liu, Mingyang Kang, Peter L. Guo","submitted_at":"2025-05-25T10:10:30Z","abstract_excerpt":"For a skew shape $\\lambda/\\mu$, we define the hybrid Grothendieck polynomial $${G}_{\\lambda/\\mu}(\\textbf{x};\\textbf{t};\\textbf{w}) =\\sum_{T\\in \\mathrm{SVRPP}(\\lambda/\\mu)} \\textbf{x}^{\\mathrm{ircont}(T)}\\textbf{t}^{\\mathrm{ceq} (T)}\\textbf{w}^{\\mathrm{ex}(T)}$$ as a weight generating function over set-valued reverse plane partitions of shape $\\lambda/\\mu$. It specializes to \\begin{itemize}\n  \\item[(1)] the refined\n  stable Grothendieck polynomial introduced by Chan--Pflueger by setting all $t_i=0$;\n  \\item[(2)] the refined dual stable Grothendieck polynomial introduced by Galashin--Grinberg--L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.19072","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/2505.19072/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"}