{"paper":{"title":"Universal Hilbert series coefficients of the superspace coinvariant ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"John Lentfer, Sylvie Corteel","submitted_at":"2026-08-08T15:28:08Z","abstract_excerpt":"The coefficients that determine the Hilbert series of the superspace coinvariant ring are indexed by hook-shaped partitions. We give a manifestly positive combinatorial interpretation of these coefficients, together with several generating functions for them. Specializing this Hilbert series at $u=-q^2$, we show that its coefficients are differences of binomial coefficients. Consequently, this proves a conjecture of Sagan--Swanson (2024) that these coefficients are palindromic up to sign. More generally, for every $m \\geq 1$ we obtain closed-form expressions for the $u = -q^m$ specialization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.08187","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/2608.08187/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"}