{"paper":{"title":"Partition Functions of Normal Factor Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"G. David Forney, Jr., Pascal O. Vontobel","submitted_at":"2011-02-01T22:47:32Z","abstract_excerpt":"One of the most common types of functions in mathematics, physics, and engineering is a sum of products, sometimes called a partition function. After \"normalization,\" a sum of products has a natural graphical representation, called a normal factor graph (NFG), in which vertices represent factors, edges represent internal variables, and half-edges represent the external variables of the partition function. In physics, so-called trace diagrams share similar features. We believe that the conceptual framework of representing sums of products as partition functions of NFGs is an important and intui"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0316","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"}