{"paper":{"title":"Multiresolution Analysis of Incomplete Rankings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Eric Sibony (LTCI), J\\'er\\'emie Jakubowicz (SAMOVAR), St\\'ephan Cl\\'emen\\c{c}on (LTCI)","submitted_at":"2014-03-08T18:16:38Z","abstract_excerpt":"Incomplete rankings on a set of items $\\{1,\\; \\ldots,\\; n\\}$ are orderings of the form $a_{1}\\prec\\dots\\prec a_{k}$, with $\\{a_{1},\\dots a_{k}\\}\\subset\\{1,\\dots,n\\}$ and $k < n$. Though they arise in many modern applications, only a few methods have been introduced to manipulate them, most of them consisting in representing any incomplete ranking by the set of all its possible linear extensions on $\\{1,\\; \\ldots,\\; n\\}$. It is the major purpose of this paper to introduce a completely novel approach, which allows to treat incomplete rankings directly, representing them as injective words over $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1994","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"}