{"paper":{"title":"Regularity of Mixed Spline Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Michael DiPasquale","submitted_at":"2014-11-08T23:59:08Z","abstract_excerpt":"We derive bounds on the regularity of the algebra $C^\\alpha(\\mathcal{P})$ of mixed splines over a central polytopal complex $\\mathcal{P}\\subset\\mathbb{R}^3$. As a consequence we bound the largest integer $d$ (the postulation number) for which the Hilbert polynomial $HP(C^\\alpha(\\mathcal{P}),d)$ disagrees with the Hilbert function $HF(C^\\alpha(\\mathcal{P}),d)=\\dim C^\\alpha(\\mathcal{P})_d$. The polynomial $HP(C^\\alpha(\\mathcal{P}),d)$ has been computed in [DiPasquale 2014], building on [McDonald-Schenck 09] and [Geramita-Schenck 98]. Hence the regularity bounds obtained indicate when a known pol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2176","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"}