{"paper":{"title":"Multivariate Hypergeometric Terms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Garth Payne","submitted_at":"2014-12-22T23:51:40Z","abstract_excerpt":"In this 1997 Ph.D. dissertation we prove a piecewise form of the discrete part of Wilf and Zeilberger's 1992 conjecture that a hypergeometric term is proper if and only if it is holonomic. We show that a holonomic hypergeometric term on $Z^n$ is piecewise proper and we show that without such a qualification the conjecture is false. We call a term piecewise proper if $Z^n$ can be expressed as the union of a finite number of polyhedral regions (the \"pieces\") and a set of measure zero (which we define to be a finite union of hyperplanes) such that the restriction of the term to each polyhedral re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7214","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"}