{"paper":{"title":"Ordered set partitions, generalized coinvariant algebras, and the Delta Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Brendon Rhoades, James Haglund, Mark Shimozono","submitted_at":"2016-09-24T06:03:43Z","abstract_excerpt":"The symmetric group $\\mathfrak{S}_n$ acts on the polynomial ring $\\mathbb{Q}[\\mathbf{x}_n] = \\mathbb{Q}[x_1, \\dots, x_n]$ by variable permutation. The invariant ideal $I_n$ is the ideal generated by all $\\mathfrak{S}_n$-invariant polynomials with vanishing constant term. The quotient $R_n = \\frac{\\mathbb{Q}[\\mathbf{x}_n]}{I_n}$ is called the coinvariant algebra. The coinvariant algebra $R_n$ has received a great deal of study in algebraic and geometric combinatorics. We introduce a generalization $I_{n,k} \\subseteq \\mathbb{Q}[\\mathbf{x}_n]$ of the ideal $I_n$ indexed by two positive integers $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07575","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":""},"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"}