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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2505.19072","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-25T10:10:30Z","cross_cats_sorted":["math.AG","math.RT"],"title_canon_sha256":"eaf2e18292bcf30f65161e9cdf76ee12cb56ed5677291a1509ab188d9a7971f0","abstract_canon_sha256":"26a057df90897d5ecfeb84725be01889a54914286a609caaece5af1d8d87a5fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:09:24.407381Z","signature_b64":"dCzuErddpaFQO9nFt8sZGxbJo/3SXEkdc6T9b7ScdfWWpznogdM0v5B5aFewlrsk1a7t0CAKYjWuYKNvCgKCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2a5590beace2bc984d30a6aa3fc2da706954705daf882480525170adb86b24a","last_reissued_at":"2026-07-05T11:09:24.406872Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:09:24.406872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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