{"paper":{"title":"Volume polynomials and duality algebras of multi-fans","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AT","math.MG"],"primary_cat":"math.CO","authors_text":"Anton Ayzenberg, Mikiya Masuda","submitted_at":"2015-09-10T04:28:40Z","abstract_excerpt":"We introduce a theory of volume polynomials and corresponding duality algebras of multi-fans. Any complete simplicial multi-fan $\\Delta$ determines a volume polynomial $V_\\Delta$ whose values are the volumes of multi-polytopes based on $\\Delta$. This homogeneous polynomial is further used to construct a Poincare duality algebra $\\mathcal{A}^*(\\Delta)$. We study the structure and properties of $V_\\Delta$ and $\\mathcal{A}^*(\\Delta)$ and give applications and connections to other subjects, such as Macaulay duality, Novik--Swartz theory of face rings of simplicial manifolds, generalizations of Min"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.03008","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"}