{"paper":{"title":"Exchangeable Hoeffding decompositions over finite sets: a characterization and counterexamples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Giovanni Peccati, Igor Pr\\\"unster, Omar El-Dakkak","submitted_at":"2012-05-23T09:35:06Z","abstract_excerpt":"We study Hoeffding decomposable exchangeable sequences with values in a finite set D. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, if the cardinality of D is strictly greater than 2, then there exists a class of neither P\\'{o}lya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable. The construction of such sequences is based on some ideas appearing in Hill, Lane and Sudderth [1987] and answers a question left open in El-Dakkak and Peccati [2008]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5138","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"}