{"paper":{"title":"Shape changing identities for permuted-basement nonsymmetric Macdonald polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guilherme Zeus Dantas e Moura, Olya Mandelshtam","submitted_at":"2026-06-01T15:43:41Z","abstract_excerpt":"Permuted-basement Macdonald polynomials $E_\\alpha^\\sigma(\\mathbf{x};q,t)$ are nonsymmetric generalizations of symmetric Macdonald polynomials that form a basis for the polynomial ring $\\mathbb{Q}(q,t)[\\mathbf{x}]$ for each fixed $\\sigma$. There are combinatorial formulas for them as generating functions over composition-shaped non-attacking fillings. In this extended abstract, we bijectively prove identities for the relationship between $E_\\alpha^\\sigma$, $E_\\alpha^{\\sigma s_i}$, $E_{s_i\\alpha}^\\sigma$, and $E_{s_i\\alpha}^{\\sigma s_i}$. These identities correspond to two combinatorial operatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02395","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/2606.02395/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"}