{"paper":{"title":"Rhombic staircase tableaux and Koornwinder polynomials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.CO","authors_text":"Lauren Williams, Olya Mandelshtam, Sylvie Corteel","submitted_at":"2023-12-29T04:40:59Z","abstract_excerpt":"In this article we give a combinatorial formula for a certain class of Koornwinder polynomials, also known as Macdonald polynomials of type $\\tilde{C}$. In particular, we give a combinatorial formula for the Koornwinder polynomials $K_{\\lambda} = K_{\\lambda}(z_1,\\dots,z_N; a,b,c,d; q,t)$, where $\\lambda = (1,\\dots,1,0,\\dots,0)$. We also give combinatorial formulas for all ``open boundary ASEP polynomials'' $F_{\\mu}$, where $\\mu$ is a composition in $\\{-1,0,1\\}^N$; these polynomials are related to the nonsymmetric Koornwinder polynomials $E_{\\mu}$ up to a triangular change of basis. Our formula"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.17469","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/2312.17469/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"}