{"paper":{"title":"Topology of Z_3 equivariant Hilbert schemes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CO","authors_text":"Deborah Castro, Dustin Ross","submitted_at":"2018-10-12T22:44:03Z","abstract_excerpt":"Motivated by work of Gusein-Zade, Luengo, and Melle-Hern\\'andez, we study a specific generating series of arm and leg statistics on partitions, which is known to compute the Poincar\\'e polynomials of Z_3-equivariant Hilbert schemes of points in the plane, where Z_3 acts diagonally. This generating series has a conjectural product formula, a proof of which has remained elusive over the last ten years. We introduce a new combinatorial correspondence between partitions of n and {1,2}-compositions of n, which behaves well with respect to the statistic in question. As an application, we use this co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05750","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":""},"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"}