{"paper":{"title":"Ordered set partitions and the 0-Hecke algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, Jia Huang","submitted_at":"2016-11-04T02:51:43Z","abstract_excerpt":"Let the symmetric group $\\mathfrak{S}_n$ act on the polynomial ring $\\mathbb{Q}[\\mathbf{x}_n] = \\mathbb{Q}[x_1, \\dots, x_n]$ by variable permutation. The coinvariant algebra is the graded $\\mathfrak{S}_n$-module $R_n := {\\mathbb{Q}[\\mathbf{x}_n]} / {I_n}$, where $I_n$ is the ideal in $\\mathbb{Q}[\\mathbf{x}_n]$ generated by invariant polynomials with vanishing constant term. Haglund, Rhoades, and Shimozono introduced a new quotient $R_{n,k}$ of the polynomial ring $\\mathbb{Q}[\\mathbf{x}_n]$ depending on two positive integers $k \\leq n$ which reduces to the classical coinvariant algebra of the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01251","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}