{"paper":{"title":"The one-sided cycle shuffles in the symmetric group algebra","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.PR","math.RT"],"primary_cat":"math.CO","authors_text":"Darij Grinberg, Nadia Lafreni\\`ere","submitted_at":"2022-12-12T22:50:40Z","abstract_excerpt":"We study a family of shuffling operators on the symmetric group $S_n$, which includes the top-to-random shuffle. The general shuffling scheme consists of removing one card at a time from the deck (according to some probability distribution) and re-inserting it at a (uniformly) random position further below. Rewritten in terms of the group algebra $\\mathbb{R}[S_n]$, our shuffle corresponds to right multiplication by a linear combination of the elements \\[t_i:=\\text{cyc}_{i}+\\text{cyc}_{i,i+1}+\\text{cyc}_{i,i+1,i+2}+\\cdots+\\text{cyc}_{i,i+1,\\ldots,n}\\in \\mathbb{R}[S_n]\\] for all $i\\in\\{1,2,\\ldot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.06274","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2212.06274/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}