{"paper":{"title":"Local limits of descent-biased permutations and trees","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Paul Th\\'evenin, Stephan Wagner","submitted_at":"2023-12-18T13:24:28Z","abstract_excerpt":"We study two related probabilistic models of permutations and trees biased by their number of descents. Here, a descent in a permutation $\\sigma$ is a pair of consecutive elements $\\sigma(i), \\sigma(i+1)$ such that $\\sigma(i) > \\sigma(i+1)$. Likewise, a descent in a rooted tree with labelled vertices is a pair of a parent vertex and a child such that the label of the parent is greater than the label of the child. For some nonnegative real number $q$, we consider the probability measures on permutations and on rooted labelled trees of a given size where each permutation or tree is chosen with a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.11183","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/2312.11183/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"}