{"paper":{"title":"Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Ewain Gwynne, Jacopo Borga, William Da Silva","submitted_at":"2023-03-29T21:21:08Z","abstract_excerpt":"The Brownian separable permutons are a one-parameter family -- indexed by $p\\in(0,1)$ -- of universal limits of random constrained permutations. We show that for each $p\\in (0,1)$, there are explicit constants $1/2 < \\alpha_*(p) \\leq \\beta^*(p) < 1$ such that the length of the longest increasing subsequence in a random permutation of size $n$ sampled from the Brownian separable permuton is between $n^{\\alpha_*(p) - o(1)}$ and $n^{\\beta^*(p) + o(1)}$ with probability tending to 1 as $n\\to\\infty$. In the symmetric case $p=1/2$, we have $\\alpha_*(p) \\approx 0.812$ and $\\beta^*(p)\\approx 0.975$. W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.17030","kind":"arxiv","version":3},"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/2303.17030/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"}