{"paper":{"title":"Random Subwords and Pipe Dreams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Colin Defant","submitted_at":"2024-08-09T17:12:24Z","abstract_excerpt":"Fix a probability $p\\in(0,1)$. Let $s_i$ denote the transposition in the symmetric group $\\mathfrak{S}_n$ that swaps $i$ and $i+1$. Given a word $\\mathsf{w}$ over the alphabet $\\{s_1,\\ldots,s_{n-1}\\}$, we can generate a random subword by independently deleting each letter of $\\mathsf{w}$ with probability $1-p$. For a large class of starting words $\\mathsf{w}$ -- including all alternating reduced words for the decreasing permutation -- we compute precise asymptotics (as $n\\to\\infty$) for the expected number of inversions of the permutation represented by the random subword. This result can also"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.05182","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.05182/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"}