{"paper":{"title":"Combinatorial proofs of Petrie Pieri rule and Plethystic Pieri rule","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kuo-Han Ku, Saintan Wu, Sen-Peng Eu, Yu-Sheng Shih","submitted_at":"2025-09-21T01:47:43Z","abstract_excerpt":"Petrie symmetric functions $G(k,n)$, also known as truncated homogeneous symmetric functions or modular complete symmetric functions, form a class of symmetric functions interpolating between the elementary symmetric functions $e_n$ and the homogeneous symmetric functions $h_n$. Analogous to the Pieri rule for $s_\\mu h_n$ and the dual Pieri rule for $s_\\mu e_n$, Grinberg showed that the Schur coefficients for the ``Pieri rule'' of $s_\\mu G(k,n)$ can be determined by the determinant $\\mathbf{pet}_k(\\lambda,\\mu)$ of Petrie matrices. Cheng, Chou, Eu, Fu, and Yao provided a ribbon tiling interpret"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.16872","kind":"arxiv","version":2},"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/2509.16872/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"}